Question

The fourth term of an ap is 11 the sum of 5th and 7th term of an ap is 34 find its common difference

Answer 1

Let first term be a and common difference be d
$given \: \: T4 = 11 \\ a + 3d = 11 - - - (1) \\ given \: \: T5 + T7 = 34 \\ (a + 4d) + (a + 6d) = 34 \\ 2a + 10d = 34 \\ a + 5d = 17 - - - (2) \\ (2) - (1) \: \: gives \\ 2d = 6 \\ d = 3$

Answer 2

Refers to attachment ☻☻