Question

In an arithmetic progression, the fourth term is 8 and the sum of 12 terms is 156. Find the value of 'p' if the {{p}^{th}}
term is 1000.
A) 200 B) 500 C) 300 D) 100

Answer 1

the fourth term is 8
8 = a + 3d (1)

sum of 12 terms is 156

156 = 12/2(2a + 11d)
26= 2a + 11d (2)
Solve (1) & (2)
Multiply (1) by 2 and subtract from (2)
10= 5d
d = 2

put in (1)
8 - 3*2 = a
a = 2

Now,
1000= a + (p-1)d
1000 = 2 + (p-1)2
500 = 1 + p - 1
p = 500

Option B is correct