Question

An a.p consists of 31 terms of its 16th term is m then the sum of all the terms
16m . 62m 31m 31/2m which one is the answer

Answer 1

Answer:

Sum of all terms S₃₁ = 31m

Step-by-step explanation

Given :

n = 31

a₁₆ = m      

Formulae Used :

$a_{n}$ = a + (n-1) d

$S_{n}$ = $\frac{n}{2}$ [2a + (n-1)d]

a₁₆ = m

∴ a + 15 d = m   -----(1)

and

S ₃₁ = 31/2 [2a + 30d]

        = 31 [a + 15d]

        = 31 m         [ from (1)]