Question

Determine an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

Answer 1

this is the correct answer

Answer 2

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

2

=> 20+6d= (20+22d)

2

=> 20+6d=10+11d

=> d=2

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

Therefore, the required AP will be 5,7, 9, 11,......