Question

The first term of an A.P. is 5 and its 100th term is - 292. Find the 50th term of this A.P.

Answer 1

D = -9 , a 50= - 1040 answer a= -5999

Answer 2

50th term = -142

Step-by-step explanation:

Given: First term of an A.P. is 5 and its 100th term is - 292.

Find:  50th term of this A.P.

Solution:  

Let the A.P. be a, a+d, a+2d..... a+nd

We know that a1 = 5 and a100 = -292

an = a1 + (n-1)d

a100 = a1 + (100-1)d  

5 +99d = -292

99d = -297

 d = -297/99

 d = -3

50th term = a1 + (50-1)d

     = 5 + 49(-3)

     = 5 - 147

     = -142