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QUESTION: 1

Find the 15th term of an arithmetic progression whose first term is 2 and the common difference is 3

Solution:

QUESTION: 2

What is the sum of the first 15 terms of an A.P whose 11 th and 7 th terms are 5.25 and 3.25 respectively

Solution:

QUESTION: 3

If(1^{2}+2^{2}+3^{2}+…..+10^{2})=385,then the value of (2^{2}+4^{2}+6^{2} + …+20^{2}) is :

Solution:

(1^{2}+2^{2}+3^{2}+.......10^{2})=385

(2^{2}+4^{2}+6^{2}+.......+20^{2}) = 2^{2}(1^{2}+2^{2}+ 3^{2}+.....+10^{2} )

=4(385)

=1540

QUESTION: 4

In an arithmetic series consisting of 51 terms, the sum of the first three terms is 65 and the sum of the middle three terms is 129. What is the first term and the common difference of the series?

Solution:

QUESTION: 5

The sum of the first 100 numbers, 1 to 100 is divisible by

Solution:

QUESTION: 6

How many terms are there in G.P 3,6,12,24,….,384?

Solution:

QUESTION: 7

Four angles of a quadrilateral are in G.P. Whose common ratio is an intiger. Two of the angles are acute while the other two are obtuse. The measure of the smallest angle of the quadrilateral is

Solution:

QUESTION: 8

How many numbers between 11 and 90 divisible by 7?

Solution:

QUESTION: 9

If Sn denotes the sum of the first n terms in an Arithmetic Progression and S1: S4 = 1: 10

Then the ratio of first term to fourth term is:

Solution:

QUESTION: 10

The sum of the three numbers in A.P is 21 and the product of their extremes is 45. Find the numbers.

Solution:

Let the numbers are be a - d, a, a + d

Then a - d + a + a + d = 21

3a = 21

a = 7

and (a - d)(a + d) = 45

a^{2} - d^{2} = 45

d^{2} = 4

d = __+__2

Hence, the numbers are 5, 7 and 9 when d = 2 and 9, 7 and 5 when d = -2. In both the cases numbers are the same.

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