Question

In an A.P., the first term is -4, the last term is 29 and the sum of all its terms is 150. Find its
common difference.

Answer 1

since n=12
An = a+(n-1)d
29=-4+11d
33=11d
d=3

Answer 2

First term, a = - 4

Last term, l = 29

Sn = 150

An = L

An = a + ( n - 1 ) d

29 = - 4 + ( n - 1 ) d

29 + 4 = ( n - 1 ) d

( n - 1) d = 33 -->( i )

Sn = 150 = n /2 [ 2 ( - 4) + ( n - 1) d]

Putting value of ( n - 1 ) d from equation ( i ),

150 = n/2 [ - 8 + 33]

150 × 2 = n ( 25 )

n = 300 / 25

n = 12

Total number of terms, n = 12

Putting value of " n" in equation ( i ),

( n - 1) d = 33

( 12 - 1 ) d = 33

11d = 33

d = 33/11 = 3

So, Common Difference, $\sf{\huge {d \:= \:3}}$