Question

find the common difference of an A.P.whose first term is 5 and the sum of first four term is half the sum of the next four term.​

Answer 1

Answer:

the common difference is 2

Step-by-step explanation:

given first term a = 5, let common difference be d

Sum(n) = (2a + (n-1)d)n/2

s1 = Sum(first 4) = Sum(4) = (2(5) + d(4-1))4/2 =  2(10 + 3d) = 20 + 6d

s2 = Sum(next 4) = Sum(8) - Sum(4) = (2(5)+d(8-1))8/2 - (20 + 6d)

= 4(10 + 7d) - 20 - 6d = 40 - 20 + 28d - 6d = 20 + 22d

given s2 = 2(s1)

20 + 22d = 2(20 + 6d)

20 + 22d = 40 + 12d

10d = 20, d = 2