Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers Chapter 9 Sequences and Series.

## Kerala Plus One Maths Chapter Wise Previous Questions Chapter 9 Sequences and Series

### Plus One Maths Sequences and Series 3 Marks Important Questions

Question 1.

Consider the GP 3,3^{2},3^{3}, _______. (IMP-2014)

i) Find the sum to n terms of this GP.

ii) Find the value of n so that the sum to n terms of this GP is 120.

Answer:

i)

ii)

### Plus One Maths Sequences and Series 4 Marks Important Questions

Question 1.

Given sum of three consecutive terms in an AP is 21 and their product is 280 (IMP-2011)

i) Find the middle term of the above terms.

ii) Find the remaining two terms of the above AP.

Answer:

i) Let the three consecutive terms be

a-d, a, a + d

a-d + a + a + d = 21

=>3a = 21

=>a = 7

ii) Then the AP becomes 7 – d,7, 7 + d

Given product is 280;

(7 – d)(7)(7 + d) = 280

=> (7 – d)(7 + d) = 40

==> 49 – d² = 40

=> <d² = 9 => d= 3,- 3

Therefore the AP is 4,7,10 or 10,7,4.

Question 2.

Consider the GP 3,6,12 (IMP-2011)

i) Which term of this GP is 96?

ii) Find the value of n so that sum to n terms of this GP is 381.

Answer:

Question 3.

i) What is the sum of the first ‘n’ natural numbers? (IMP-2012)

ii) Find the sum to ‘n’ terms of the series

3 x 8 + 6 x 11 + 9 x 14 + ______.

Answer:

Question 4.

If the sum of the first n terms of an Arithmetic progression is ——,where X and Y are constants, find (IMP-2012)

i) S_{1} and S_{2}

ii) The first term and common difference.

iii) The n^{th} term.

Answer:

i) S_{1} = X

S_{2} =2X + 1/2(2 – 1)Y=2X + Y

ii) First term = a, = Sx = X

S_{2} =2 X + Y

=> a_{1} +a_{2} =2 X + Y

=> a_{2} =2X + Y

=>a_{2} = X+ Y

Common difference =

a_{2} – a_{1} =X + Y – X = Y

iii) n^{th}term = a_{n} = a + (n-1)d = X + (n – 1)Y

Question 5.

Find the sum to n terms of the series; (IMP-2012)

2² + 5² + 8² +_______

Answer:

Question 6.

i) Write the first four terms of the sequence whose nth term \(a_{n}=\frac{n}{n+1}\) (MARCH-2013)

ii) The sum of the first three terms of a GP is \(\frac {12}{13}\) and their product is -1. Find the common ratio and the terms.

Answer:

Question 7.

If the numbers \(\frac { 5 }{ 2 }\) x \(\frac { 5 }{ 8 }\) are three consecutive terms of a GP, then find x. (MARCH-2014)

Find the sum of the first n-terms of the series. 2 +22+222 + _____

Answer:

Question 8.

i) Find the 5^{th} term of the sequence whose nth term is \(a_{n}=\frac{n(n-2)}{(n+3)}\) (MARCH-2014)

ii) Write the sum of first n natural numbers.

iii) The 5^{th}, 8^{th} and 11^{th} terms of a GP are p, q and s respectively. Prove that q^{2} – ps

Answer:

Question 9.

i) A man starts repaying a loan as a first instalment of Rs. 1,000. If he increases the instalment by Rs. 150 every month, what amount will he pay in the 30^{th} instalment? (IMP-2014)

ii) Find the sum to n terms of the sequence:

7,77,777,7777 ______.

Answer:

Question 10.

i) Consider the AP 4,10,16,22…….. Find its common difference and the 7^{th} terms. (IMP-2014)

ii) If the m^{th} term of an AP is \(\frac { 1 }{ n }\) and the nth term is \(\frac { 1 }{ m }\) , prove that the sum of the first ‘mn’ terms is \(\frac { 1 }{ 2 }\)(mn +1)

Answer:

Question 11.

The 6^{th} term of the sequence whose n^{th} term is \(t_{n}=\frac{2 n-3}{6}\) is _____. (MARCH-2015)

a) 3

b) \(\frac { 1 }{ 2 }\)

c) \(\frac { 3 }{ 2 }\)

d) \(\frac { 1 }{ 3 }\)

ii) Find the sum to infinity of the sequence 1,\(\frac { 1 }{ 3 }\) ,\(\frac { 1 }{ 9 }\), ………

iii) If a, b, c are in AP and \(a^{\frac{1}{x}}=b^{\frac{1}{y}}=c^{\frac{1}{z}}\), prove that x, y, z are in AP.

Answer:

### Plus One Maths Sequences and Series 6 Marks Important Questions

Question 1.

i) In an AP, the first term is 2 and the sum of the first five terms is one fourth the sum of the next five terms. (MARCH-2010)

a) Find the common difference.

b) Find the 20^{th} term.

ii) If AM and GM of two numbers are 10 and 8 respectively, find the numbers.

Answer:

Question 2.

i) In an AP if m^{th} term is ‘n’ and nth term is ‘m’ .find the (m + n)^{th} term. (IMP-2010)

ii) If 3^{rd}, 8^{th} and 13^{th} terms of a GP are x,y,z respectively, prove that x,y,z are in GP.

iii) Prove that x,y,z in the above satisfies the equation \(\frac{y^{10}}{(x z)^{5}}=1\)

Answer:

Question 3.

Which of the following is the n^{th} term of an AP? (MARCH-2011)

a) 3 – 2n

b)n² – 3

c) 3^{n} – 2

d) 2 – 3n²

ii) Find the 10th term of the sequence

– 6,- \(\frac { 11 }{ 2 }\), – 5,….

iii) The sum of the first three terms of a GP is \(\frac { 39 }{ 10 }\) and their product is 1. Find the common ratio and the terms.

Answer:

Question 4.

Find the 10^{th} term of an AP whose n^{th} \(\frac{2 n-3}{6}\) term is (MARCH-2012)

ii) Find the sum of the first 10 terms of the above AP.

iii) Find the sum of the first 10 terms of a GP, whose 3^{rd} term is 12 and 8^{th} term is 384.

Answer:

Question 5.

i) Find the 5^{th} term of the sequence whose n^{th} term, \(a_{n}=\frac{n^{2}-5}{4}\) (MARCH-2013)

ii) Find 7 + 77 + 777 +……. to n terms.

iii) Find the sum to n terms of the series.

1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ………

Answer:

Question 6.

i) Find the sum of multiple of 7 between 200 and 400. (IMP-2013)

ii) The sum of first 3 terms of a GP is \(\frac { 39 }{ 10 }\) and their product is 1. Find the terms.

Answer:

Question 7.

If ‘a’ is the first term and ‘cf is the common difference of an AP, then the nth term of the AP, a_{n} = ……. (MARCH-2014)

ii) In an AP, if the m^{th}‘ term is ‘n’ and the n^{th} term is ‘m’, where , prove that its p^{th} term is n + m – p.

iii) Find the sum to ‘n’ terms of the series:

1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + _______.

Answer:

Question 8.

i) If the sum of certain number of terms of the AP 25,22,19 is 116, then find the last term. (IMP-2014)

ii) Find the sum to n terms of the series

1 x 2 x 3 + 2 x 3 x 4 + 3 x 4 x 5 + ………

(Imp (Science) – 2014)

Answer:

Question 9.

i) The 3^{rd} term of the sequence whose n^{th} term is (MARCH-2015)

ii) Insert three numbers between 1 and 256 so that the resulting sequence is a GP.

iii) If p^{th} term of an AP is q and q^{th} term is ‘p’, where p ≠ qfind r^{th} term.

Answer:

Question 10.

i) Geometric mean of 16 and 4 is ______. (IMP-2015)

(a) 20

(b) 4

(c) 10

(d) 8

ii) Find the sum to n terms of the series: 5 + 55 + 555 + ________.

iii) Find the sum to n terms of the AP,

whose K^{th} term is a_{k} = 5K +1

Answer:

Question 11.

i) If the first three terms of an AP is x – 1,x + 1, 2x + 3, then x is (IMP-2015)

(a)- 2

(b) 2

(c) 0

(d) 4

ii) Find the sum to n terms of the sequence.

1 x 2 + 2 x 3 + 3 x 4 + _______

iii) The nth term of the GP 5,- \(\frac { 5 }{ 2 }\),\(\frac { 5 }{ 4 }\),\(\frac { 5 }{ 8 }\),….. is \(\frac { 5 }{ 1024 }\) find ‘n’.

Answer:

Question 12.

The n^{th} term of the GP 5,25,125 (MARCH-2016)

is

(a) n^{5}

(b) 5^{n}

(c) (2n)^{5}

(d) (5)^{2n}

ii) Find the sum of .all natural numbers between 200 and 1000 which are multiples of 10.

iii) Calculate the sum of n-terms of the series whose n81 term is a_{n} = n(n + 3)

Answer:

Question 13.

i) Which among the following represents the sequence whose n^{th} terms is \(\frac { n}{ n+1 }\) ? (MAY-2017)

a) 1,2,3,4,5,6

b) 2,3,4,5,6

c) 2,\(\frac { 3 }{ 2 }\),\(\frac { 4 }{ 3 }\),\(\frac { 5 }{ 4 }\),\(\frac { 6 }{ 5 }\)

d) \(\frac { 1 }{ 2 }\),\(\frac { 2 }{ 3 }\),\(\frac { 3 }{ 4 }\),\(\frac { 4 }{ 5 }\),\(\frac { 5 }{ 6 }\)

ii) Using progression, find the sum of first five terms of the series 1 + \(\frac { 2 }{ 3 }\) + \(\frac { 4 }{ 9 }\) + …..

iii) Calculate: 0.6 + 0.66 + 0.666 + ………. n terms.

Answer:

Question 14.

The sum of the infinite series is 1, \(\frac { 1 }{ 3 }\),\(\frac { 1 }{ 9 }\) ………is ________. (MARCH-2017)

(a) \(\frac { 3 }{ 2 }\)

(b) \(\frac { 5 }{ 2 }\)

(c) \(\frac { 2 }{ 3 }\)

(d) \(\frac { 7 }{ 2 }\)

ii) Find the sum of all natural numbers between 100 and 1000 which is a multiple of 5.

iii) Find the sum to n terms of the series 8,88,888 ………

Answer:

Question 15.

The 6^{th} term of the GP \(\frac { 1 }{ 2 }\),\(\frac { 1 }{ 4 }\),\(\frac { 1 }{ 8 }\), ………. (MARCH-2017)

a) \(\frac { 1 }{ 32 }\)

b) \(\frac { 1 }{ 64 }\)

c) \(\frac { 1 }{ 16 }\)

d) \(\frac { 1 }{ 128 }\)

ii) The sum of 1st 3 terms of a G.P is \(\frac { 13 }{ 12 }\) and their product is – 1. Find the common ratio and terms.

iii) Find the sum to n terms of the series \(3 \times 1^{2}+5 \times 2^{2}+7 \times 3^{2}\) + ………

Answer: