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

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 3,32,33, _______. (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.
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.
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.

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 + ______.

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) S1 and S2
ii) The first term and common difference.
iii) The nth term.
i) S1 = X
S2 =2X + 1/2(2 – 1)Y=2X + Y
ii) First term = a, = Sx = X
S2 =2 X + Y
=> a1 +a2 =2 X + Y
=> a2 =2X + Y
=>a2 = X+ Y
Common difference =
a2 – a1 =X + Y – X = Y
iii) nthterm = an = a + (n-1)d = X + (n – 1)Y

Question 5.
Find the sum to n terms of the series;  (IMP-2012)
2² + 5² + 8² +_______

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.

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 + _____

Question 8.
i) Find the 5th 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 5th, 8th and 11th terms of a GP are p, q and s respectively. Prove that q2 – ps

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 30th instalment?  (IMP-2014)
ii) Find the sum to n terms of the sequence:
7,77,777,7777 ______.

Question 10.
i) Consider the AP 4,10,16,22…….. Find its common difference and the 7th terms.  (IMP-2014)
ii) If the mth 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)

Question 11.
The 6th term of the sequence whose nth 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.

### 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 20th term.
ii) If AM and GM of two numbers are 10 and 8 respectively, find the numbers.

Question 2.
i) In an AP if mth term is ‘n’ and nth term is ‘m’ .find the (m + n)th term.  (IMP-2010)
ii) If 3rd, 8th and 13th 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 $$\frac{y^{10}}{(x z)^{5}}=1$$

Question 3.
Which of the following is the nth term of an AP? (MARCH-2011)
a) 3 – 2n
b)n² – 3
c) 3n – 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.

Question 4.
Find the 10th term of an AP whose nth $$\frac{2 n-3}{6}$$ 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 3rd term is 12 and 8th term is 384.

Question 5.
i) Find the 5th term of the sequence whose nth 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 + ………

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.

Question 7.
If ‘a’ is the first term and ‘cf is the common difference of an AP, then the nth term of the AP, an = ……. (MARCH-2014)
ii) In an AP, if the mth‘ term is ‘n’ and the nth term is ‘m’, where , prove that its pth 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 + _______.

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)

Question 9.
i) The 3rd term of the sequence whose nth term is (MARCH-2015)
ii) Insert three numbers between 1 and 256 so that the resulting sequence is a GP.
iii) If pth term of an AP is q and qth term is ‘p’, where p ≠ qfind rth term.

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 Kth term is ak = 5K +1

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’.

Question 12.
The nth term of the GP 5,25,125 (MARCH-2016)
is
(a) n5
(b) 5n
(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 an = n(n + 3)

Question 13.
i) Which among the following represents the sequence whose nth 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.

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 ………
The 6th 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 $$3 \times 1^{2}+5 \times 2^{2}+7 \times 3^{2}$$ + ………