Question

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.

Answer 1

Let the common difference of the AP be d.

First term, a = 5

Now,

a₁ + a₂ + a₃ + a₄ = \(\frac{1}{2}\)(a₅ + a₆ + a₇ + a₈)    (Given) 

\(\Rightarrow\) 8a + 12d = 4a + 22d

\(\Rightarrow\) 22d - 12d = 8a - 4a

\(\Rightarrow\) 10d = 4a

\(\Rightarrow\) \(d=\frac{2}{5}a\)

\(\Rightarrow\) \(d=\frac{2}{5}\times5=0\) (a = 5)

Hence, the common difference of the AP is 2.