Question

Obtain the sum of the first 56 terms of an A.P. whose 18^th and 39^th terms are 52 and 148 respectively.

Answer 1

t₁₈ = 52 and t₃₉ = 148 S₅₆ = ? 

t_n = a + (n-1)d

t₁₈ = a +( 18 - 1) d 

52 = a + 17 d     ......(i) 

t₃₉ = a + (39 -1) d

∴ 148 = a + 38d   ........(2) 

Adding (1) and (2) 

a + 17d = 52

a + 38d = 148 

2a = 55d = 200 .......(3)

S_n = `n/2` [2a + (n - 1) d ]

S₅₆ = `56/2` [2a + (56 -1) d] 

      = 28 [2a + 55d ]

      = 28(200) [from eq (3)]

S₅₆  = 5600