Question

34. Find the common difference of an AP whose first term is 5 and the sum
of its first four terms is half the sum of the next four terms.
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Answer 1

Answer:

Let d is common difference of AP

Now first 4 terms are 5, 5+d, 5+2d, 5+3d

and next 4 terms 5+4d, 5+5d, 5+6d, 5+7d

Given that, the sum of its first four terms is half the sum of the next four terms.

i.e.,

5 + 5+d + 5+2d + 5+3d=

2

5+4d + 5+5d + 5+6d + 5+7d

20+6d=

2

(20+22d)

20+6d=10+11d

d=2

Hence, the common difference of the given A.P. is 2

Answer 2

Explanation:

Let d is common difference of AP

Now first 4 terms are 5, 5+d, 5+2d, 5+3d

and next 4 terms 5+4d, 5+5d, 5+6d, 5+7d

Given that, the sum of its first four terms is half the sum of the next four terms.

i.e.,

5 + 5+d + 5+2d + 5+3d=

2

5+4d + 5+5d + 5+6d + 5+7d

20+6d=

2

(20+22d)

20+6d=10+11d

d=2

Hence, the common difference of the given A.P. is 2