Question

The first and the last term of an AP are –4 and 146. The sum of the terms is 7171.

The number of terms is

Answer 1

Given,

First term ( a ) = -4

Last term ( l ) = 146

Sum of all terms = 7,171

Let , the number of terms is n.

⇒Sum of n terms = ( n/2 ) ( First term + Last term )


⇒ 7,171 = ( n/2 ) ( -4 + 146 )


⇒ 7,171 = ( n/2 ) ( 142 )

⇒ 7,171 = 71n

⇒ n = 7,171 ÷ 71

•°• n = 101

So, this A.P. has 101 terms.

Answer 2

a1=-4
an=146
Sn=7171

an=a+(n-1)d
150=(n-1)d

7171=n/2(2a+(n-1)d)
101=n


no. of terms are 101

d

150=(n-1)d
put value of n
d=3/2...


hope it will help...