Question

The sum of 5th and 7th term of an AP is 52 and the 10th term is 46. Find the common difference.

Answer 1

a + 9d = 46 ------------(1)

s(5) = 5/2(2a+4d) = 5(a+2d)

s(7) = 7/2(2a+6d) = 7(a+3d)

(5a+10d) + (7a+21d) = 52

12a + 31d = 52 ------------(2)

solving both equation ,

77d = 500

d = (500/77) [ Ans.]

Answer 2

SOLUTION:-

Given:

The sum of 5th & 7th term of an A.P. is 52 & the 10th term is 46.

To find:

The common difference.

Explanation:

Assume the first term & common difference of A.P. are a & d, respectively

•First term= a

•Common difference=d

According to the question:

a5 + a7= 52.

a10 = 46

Formula of the Arithmetic Progression:

${}^{a} n = a + (n - 1)d$

=) a+(5-1)d +a+(7-1)d =52

=) a+ 4d + a +6d =52

=) 2a + 10d = 52

=) a + 5d = 26..............(1)

&

=) a + (10-1) d= 46

=) a + 9d =46...............(2)

On subtracting equation (1) from equation (2), we get;

=) (a +9d) -(a+5d) = 46 -26

=) a +9d -a - 5d = 20

=) a -a +9d -5d = 20

=) 4d = 20

=) d = 20/4

=) d= 5

Thus,

The common difference is 5.

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