Question

Find the common difference of an A.P. whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

Answer 1

Let common difference = x
First term = 5
Hence next term will be 5 , (5 + x) (5 + 2x) (5 + 3x) (5 + 4x) (5 + 5x) (5 + 6x) (5 + 7x) (5 + 8x)
Sum of first four terms = 5 + 5 + x + 5 + 2x + 5 + 3x = 20 + 6x
Sum of next four terms = 5 + 4x + 5 + 5x + 5 + 6x + 5 + 7x + 5 + 8x = 20 + 22x
Now, Sum of first four terms is 1/2 of next four terms sum
⇒(20 + 6x)2 = (20 + 22x)
⇒ 40 + 12x = 20 + 22x
⇒ 12x − 22x = 40 − 20
⇒ 10x = 20
⇒ x = 2