Question

The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference.

Answer 1

Let a and d be the first term and the common difference of the AP, respectively.

∴ n^th term of the AP, a_n  = a + (n − 1)d

Given:

\[a_4 = 11\]

\[\Rightarrow a + \left( 4 - 1 \right)d = 11\]
\[ \Rightarrow a + 3d = 11 . . . . . \left( 1 \right)\]

Also, \[a_5 + a_7 = 34\]

\[\Rightarrow \left( a + 4d \right) + \left( a + 6d \right) = 34 \]

\[ \Rightarrow 2a + 10d = 34\]

\[ \Rightarrow a + 5d = 17 . . . . . \left( 2 \right)\]

Solving (1) and (2), we get
a = 2 and d = 3
Hence, the common difference of the AP is 3.