Question

obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are
52 and 148 respectively.
(1) Using t18 and t39 find two simultaneous equation in variables a and d
(2) using these equations find s56​

Answer 1

Answer:

Step-by-step explanation:

t18=a+17d=52

t39=a+38d=148

add both equations

2a+55d=200........1

S56=56/2(2a+(n_1)d)

=28(2a+55d)

=28*200 from1

=5600

Answer 2

Answer:

Let us assume the first term to be = a

and common difference be = d

so,

a₁₈ = a + 17d  

⇒ 52 = a + 17d.........................(1)

a₃₉ = a + 38d

⇒ 148 = a + 38d...............................(2)

Solving (1) and (2) by elimination method, we get,

d = 32/7

Now substituting d = 32/7 in (1), we get,

a = 52 - 17(32)/7

⇒ a = 180/7

S₅₆ = 56/2{2 x(180/7) + 55(32/7)}

     = 28 x (360 + 1760/7)

     = 28 x (2120/7)

     = 4 x 2120

     = 8480  

Hence the sum of first 56 terms is 8480.

Hope it helps you.....