Students often refer to SSLC Maths Textbook Solutions and Class 10 Maths Chapter 1 Arithmetic Sequences Important Extra Questions and Answers Kerala State Syllabus to clear their doubts.
SSLC Maths Chapter 1 Arithmetic Sequences Important Questions and Answers
Arithmetic Sequences Class 10 Extra Questions Kerala Syllabus
Arithmetic Sequences Class 10 Kerala Syllabus Extra Questions
Question 1.
x, y, z are the three consecutive terms of an arithmetic sequence. Which of the following is correct?
(a) y = x + z
(b) 2y = x + z
(c) y = x – z
(d ) x = y + z
Answer:
(b) 2y = x + z
Question 2.
The first three digit term of the arithmetic sequence 1, 6, 11, 16 …….. is
(a) 101
(b) 102
(c) 100
(d) 103
Answer:
(a) 101
Question 3.
13th term of an arithmetic sequence is 20. What is the sum of Is’ and 25s’ term?
(a) 30
(b) 50
(c) 40
(d) 20
Answer:
(c) 40
Question 4.
Distance from 10” term to 15:,: term is 11. What is the distance from 10;- term to 20,r- term?
(a) 33
(b) 10
(c) 22
(d) 20
Answer:
(c) 22
Question 5.
The position at which 100 becomes a term of the sequence \(\frac{1}{7}, \frac{2}{7}, \frac{3}{7}\)
(a) 100
(b) 300
(c) 700
(d) 200
Answer:
(c) 700
Question 6.
a, a – 1, a – 2, a – 3 is an arithmetic sequence.
a) What is the common difference of the sequence ?
b) What is its 10th term?
Answer:
a) Common difference = – 1
b) a – 9
Question 7.
10th term of an arithmetic sequence is 25 and its common difference 4
a) What is the 15th term?
b) What is the 5th term?
Answer:
a) 15th term = 10th term + 5 × common difference
= 25 + 5 × 4 = 45
b) 5th term = 10th term – 5 × common difference = 25 – 20 = 5
Question 8.
Sum of the 7 consecutive terms of an arithmetic sequence is 119.
a) Which term comes in the middle of these 7 terms?
b) What is the sum of two terms on either side of the middle term just closer to it?
Answer:
a) -y = 17
b) 2 × 17 = 34
Question 9.
Common difference of an arithmetic sequence is \(\frac{1}{2}\)
a) What is the difference between 5th term and 15th term?
b) If 5th term is 20 then what is the first term of the sequence?
Answer:
a) Difference is 10 times common difference. It is 10 × \(\frac{1}{2}\) = 5
b) First term = 5th term – 4 times common difference = 20 – 4 × \(\frac{1}{2}\) = 18
Question 10.
□ , 10, □ , □ , 31 are five consecutive terms of an arithmetic sequence.
a) What is the common difference ?
b) Write the terms in the boxes.
Answer:
a) Difference between second term and fifth term is three times common difference
3 × common difference = 31 – 10 = 21
Common difference is \(\frac{21}{3}\) = 7
b) 3, 10, 17, 24, 31
Question 11.
Angles of a right triangle are in arithmetic sequence.
a) Which angle comes in the middle?
b) What are the angles?
Answer:
a) Middle term = \(\frac{180}{3}\) = 60
b) Largest term (third angle )= 90°. So common difference is 30°
Angles are 30°, 60°, 90°
Question 12.
Angle sum of a pentagon is 540? .The angles when arranged in the ascending order makes an arithmetic sequence.
a) Which angle comes as the middle term of the sequence?
b) If the first term is 42° then what is the difference between two adjacent terms?
Answer:
a) Middle term of the arithmetic sequence is \(\frac{540}{5}\) = 108
Middle angle is 108°
b) Difference between first term and third term is two times common difference It is 108 – 42 = 66.
Common difference is 33.
Question 13.
Common difference of an arithmetic sequence is 10
a) What is the difference between sixth term and first term?
b) Write two term positions having the same difference.
Answer:
a) Difference between sixth term and first term is five times common difference.
It is 5 × 10 = 50
b) Difference 7th term – 2nd term, 8th term – 3rd term gives the same difference.
Question 14.
Sum of the first five terms of an arithmetic sequence and sum of the first eight terms of the same arithmetic sequence are equal.
a) What is the sum of sixth, seventh and eighth terms of the sequence ?
b) What is the seventh term?
Answer:
a) 70 – 70 = 0
b) Sum of sixth , seventh , eighth term is 0. So 7th term is \(\frac{0}{3}\) = 0
Question 15.
√2, √8, √18… is an arithmetic sequence
a) What is the common difference?
b) What is the difference between first term and eleventh term?
Answer:
a) Common difference is √8 – √2 = 2√2 – √2 = √2
b) Difference is ten times common difference. It is 10√2
Question 16.
Look at the sequence of squares
a) Write the number of sticks used for making squares as sequence
b) Describe the sequence in your own words
c) How many sticks are needed to make 1O’* term?
Answer:
a) 4, 7, 10…
b) This is the sequence of numbers 1 more than multiple of 3
c) 3 × 10 + 1 = 31
Question 17.
This the sequence of triangles made by sticks
a) Write the number of sticks used for making triangles as a sequence
b) Describe this sequence in your own words.
c) How many sticks are needed to make 50th term of the sequence?
Answer:
a) 3, 5, 7…
b) This is the sequence of numbers 1 more than multiple of 2
c) 2 × 50 + 1 = 101
Question 18.
Third term of an arithmetic sequence is 12 and its fifth term20
a) What is the common difference?
b) What is the first term ?
c) Write the sequence numerically
Answer:
a) Difference between fifth term and third term is two times common difference.
2 × common difference = 20 – 12 = 8, Common difference = 4
b) First term = third term – 2 common difference = 12 – 8 = 4
c) 4, 8, 12…
Question 19.
The 4th term of an.arithmetic sequence is 54 and its 9th term is 99.
(a) What is the common difference of the sequence ?
(b) Will the difference between any two terms of this sequence be 900 ? Why ?
Answer:
a) Difference between ninth term and fourth term is five times common difference.
5 times common difference = 99 – 54 = 45, common difference is 9
(b) We know that difference between two terms of an arithmetic sequence is a multiple of common difference.
Here 900 is the multiple of 9. So 900 can be the difference between two terms.
Question 20.
The sum of 1st and 19th terms of an arithmetic se-quence is 50. The sum of its 1st and 20th terms is 54.
a) What is the common difference of the sequence ?
b) What is the sum of its 7th and 13th terms ?
c) Find its 10th term.
Answer:
a) Common difference = 54 – 50 = 4
b) Sum of 7th and 13th term is 50
c) Tenth term is = \(\frac{50}{2}\) = 25
Question 21.
700 rupees is used for purchasing 7 prizes . Cost of each prize is 20 rupees more than the cost of the prize just below it.
a) What is the cost of fourth prize?
b) What is the cost of first prize?
c) Write costs of prizes in the decending order.
Answer:
a) Fourth term = 100
b) First prize is 3 × 20 more than fourth term. It is 100 + 3 × 30= 16
c) 160, 140, 120, 100, 80, 60, 40
Question 22.
5th term of an arithmetic sequence is 10 and 10th term is 5.
a) What is the common difference of the sequence?
b) Find the first term?
c) What is its 15th term?
Answer:
a) Difference between 10th term and 5th term is five times common difference.
5 – 10 = 5 common difference
common difference = \(\frac{-5}{5}\) = -1 5
b) First term = 10 – 4 × -1 = 14
c) Fifteenth term = tenth term + 5 × common difference = 5 + -1 × 5 = 0
Question 23.
7th term of an arithmetic Sequence is 30 and common difference 3
a) What is its 13th term ?
b) What is its first term?
c) What is the sum of first 13 terms?
Answer:
7th term of an arithmetic Sequence is 30 and common difference 3
a) 13th term = seventh term + six times common difference
13th term = 30 + 6 × 3 = 48
b) First term + thireenth term = 2 × 7 th term = 60
First term = 60 – 48 = 12
OR
First term = seventh term -6 times common difference = 12
c) Sum of the first 13 terms = 390
Question 24.
Angles of a pentagon are in arithmetic sequence when arranged in the ascending order. First term is 42°
a) What is its middle term?
b) What is the difference between two adjacent terms?
c) Find the largest term of the pentagon
Answer:
a) Angle sum of a pentagon (n – 2) × 180
= 3 × 180 = 540
Middle term = \(\frac{540}{5}\) = 108
b) Difference between third term and first term is two times common difference
2 × common difference = 108 – 42 = 66,
Common difference = 33
c) Fifth term = 108 + 2 × 33 = 108 + 66 = 174
Angles are 42°, 75°, 108°, 141°, 174°
Question 25.
Eight consecutive terms of an arithmetic sequence are written as pairs taking terms equidistant from both ends (9, 58), (16, 51), (23,44), (30, 37)
a) What is the common difference of the sequence ?
b) What is the sum of these terms?
Answer:
a) 6th and 5th terms are paired as (30, 37). Common difference is 3
b) Pair sum 67. Sum of terms = 4 × 67 = 268
Question 26.
Consider the arithmetic sequence 4, 7, 10…
(a) What is its 13th term ?
(b) What is the sum of its first 25 terms ?
(c) Find the sum of first 25 terms of the arithmetic sequence 8, 14, 20
Answer:
Consider the arithmetic sequence 4, 7, 10…
(a) Thirteenth term = first term + 14 times common difference
13th term = 4 + 12 × 3 = 40
(b) Sum of first 25 terms = thireenth term × 25 = 40 × 25 = 1000
(c) Each term is two times the terms of the first sequence
Sum = 2 × 1000 = 2000
Question 27.
The sum of the first 5 terms of an arithmetic sequence is 65 and the sum of the first 9 terms is 189.
a) What is the 3rd term of the sequence ?
b) What is the 5th term of the sequence ?
c) What is the common difference of the sequence ?
Answer:
a) Third term = \(\frac{65}{5}\) = 13
b) Fifth term = \(\frac{189}{9}\) = 21
c) 2 × common difference = 21 – 13 = 8, Common difference is 4
Question 28.
7th term of an arithmetic sequence is 18 and its 18th term is 7.
a) What is the common difference of the sequence ?
b) Find the 25th term of the sequence.
c) What is the sum of first 49 terms of the sequence ?
d) What is the sum of first 50 terms of the sequence ?
Answer:
7 th term of an arithmetic sequence is 18 and its 18th term is 7.
a) 18th term – 7th term = 11 times common difference 7 – 18 = 11 × common difference,
Common difference = – 1
b) 25th term = 18th term + 7 times common difference. It is 7 + 7 × – 1 = 0
c) 25th term is 0. Sum of first 49 terms = 0
d) 50th term = 25th term + 25 times common difference. It is 0 + 25 × -1 = -25
Sum of 50 terms = sum of 49 terms + 50th term = 0 + -25 = -25
Question 29.
There are 20 terms in an arithmetic sequence. Sum of the first and last terms is 67.
a) What is the sum of 2nd and 19th term ?
b) If the 10th term is 32, What is the 11th term ?
c) What is the common difference of the sequence ?
d) What is the first term ?
Answer:
a) 67
b)35
c) 3
d) 5
Question 30.
The sum of first 9 terms of an arithmetic sequence is 144 and the sum of next 6 terms is 231.
a) What is the 5th term of the sequence ?
b) What is its 81th term ?
c) What is the common difference of the sequence?
Answer:
Solve the problem yourself.
Sum of first 9 terms is 144 . From this find its 5th term Sum of first 15 terms will be 144 + 231 = 375. Find 8th term.
Using 5th term and 8th term find the common difference