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QUESTION: 1

In an A.P., if common difference is 2, Sum of n terms is 49, 7^{th} term is 13 tthen then n = _________.

Solution:

QUESTION: 2

If 8^{th} term of an A.P. is 15, then sum of its 15 terms is

Solution:

QUESTION: 3

If the sum of n terms of an A.P. be 2n^{2} + 5n, then its 'n^{th}' term is

Solution:

QUESTION: 4

If 'n' arithmetic means are inserted between 7 & 71 and 5^{th }arithmetic mean is 27, then 'n' is equal to:

Solution:

QUESTION: 5

If the sum of n terms of an A.P. be 3n^{2} - n and its common difference is 6, then its first terms is:

Solution:

QUESTION: 6

In a G.P. the sixth term is 729 and the common difference is 3, then the first term is G.P. is:

Solution:

Sixth term is 729, common ratio r is 3

let first term be a

ar^{5} = 729

a = 729 / (3)^{5}

a = 729 / 243

so a = 3

QUESTION: 7

The 4^{th} term of an A.P. is three times the first and the 7^{th} term excessds twice the third term by 1. Find the first term 'a' and common difference 'd'.

Solution:

QUESTION: 8

The first term of a G.P. where second term is 2 and sum of infinite term is 8 will be

Solution:

QUESTION: 9

If the sum of the 4th term and the 12th term of an A.P. is 8, what is the sum of the first 15 terms of the progression?

Solution:

QUESTION: 10

An Arithmetic progression has 13 terms whose sum is 143. The third term is 5 so the first term si

Solution:

QUESTION: 11

If a_{1}, a_{2}, a_{3} represents first, second and third terms of an AP respectively, the first terms is 2 and (a_{1} + a_{2})a_{3} is minimum, then the common difference is equal to

Solution:

QUESTION: 12

If each month Rs.100 increase in any sum then find out the total sum after 10 months, if the sum of first month is Rs.2,000.

Solution:

QUESTION: 13

The sum of all two Digit odd numbers is

Solution:

QUESTION: 14

Insert two Arithmetic means between 68 and 260

Solution:

QUESTION: 15

The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.

Solution:

QUESTION: 16

Find the product of:

(243), (243)^{1/6 ,} (243)^{1/36},.........∞

Solution:

QUESTION: 17

If sum of 3 arithmetic means between "a" and 22 us 42, then "a" =____

Solution:

QUESTION: 18

The numbers x, 8, y are in G.P. and the numbers x, y, -8 are in A.P. The values of x, y are _________.

Solution:

QUESTION: 19

Divide 144 into three parts which are in AP and such that the largest is twice and smallest, the smallest of three numbers will be:

Solution:

QUESTION: 20

If Sum (S_{n}) of 'n'-terms of an Arithmetic Progression is (2n^{2}+n).What is the difference of its 10^{th} and 1^{st} terms?

Solution:

QUESTION: 21

Find the number whose arithmetic mean is 12.5 and geometric mean is 10.

Solution:

QUESTION: 22

If the sum of infinite terms in a G.P. is 2 and the sum of their squares is 4/3 the series is

Solution:

QUESTION: 23

The sum upto infinity of the series 2/3+5/9+2/27+5/81+…..is

Solution:

QUESTION: 24

Three numbers in G.P. with their sum 13/3 and sum of their squares 91/9 are _______.

Solution:

QUESTION: 25

Three numbers in G.P. with their sum 130 and their product 27000 are _________.

Solution:

QUESTION: 26

If the continued product of three numbers in G.P. is 27 and the sum of their products in pairs is 39 the numbers are_______.

Solution:

QUESTION: 27

The sum upto infinity of the series 4+0.8+0.16+…….is

Solution:

QUESTION: 28

Find five numbers in G.P. such that their product is 32 and the product of the last two is 108.

Solution:

QUESTION: 29

The sum upto infinity of the series 1/2+1/6+1/18+……is

Solution:

QUESTION: 30

The sum upto infinity of the series 4/7-5/7^{2}+4/7^{3}-5/7^{4}+……..is

Solution:

QUESTION: 31

In the given Geometric progression find the number of terms. 32, 256, 2048, 16384,.........,2^{50}.

Solution:

n^{th} term = first term(ratio^{n – 1})., 2^{50} = 2^{5}(2^{3(n-1)}), n = 15. This implies the 16^{th} term

QUESTION: 32

The infinite G.P. series with first term 1/4 and sum 1/3 is

Solution:

QUESTION: 33

The sum of n terms of the series 1.03+1.03^{2}+1.03^{3}+ ………is

Solution:

QUESTION: 34

If the first term of a G.P exceeds the second term by 2 and the sum to infinity is 50 the series is ________.

Solution:

QUESTION: 35

If the sum of n terms of a G.P. with first term 1 and common ratio 1/2 is 1+127/128, the value of n is ___________.

Solution:

QUESTION: 36

If the sum of n terms of a G.P. with last term 128 and common ratio 2 is 255, the value of n is __________.

Solution:

QUESTION: 37

The G.P. whose 3^{rd} and 6^{th} terms are 1, -1/8 respectively is

Solution:

QUESTION: 38

How many terms of the G.P. 1, 4, 16 …. are to be taken to have their sum 341?

Solution:

QUESTION: 39

The sum of n terms of the series 0.3+0.03+0.003+…… is

Solution:

QUESTION: 40

If a, b, c are in A.P. a, x, b are in G.P. and b, y, c are in G.P. then x^{2}, b^{2}, y^{2} are in

Solution:

### Arithmetic progressions

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### Introduction - - Arithmetic Progressions (AP)

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