Question

In an AP , the first term is -4 and the last term is 29 and the sum of all its term is 150. find its common difference

Answer 1

Answer:

3

Step-by-step explanation:

29 = -4 + (n-1)d

33=( n-1)d

150 = n/2 (-8 + 33)

6 = n/2

n = 12

33 = 11 x d

d = 3

Answer 2

a = -4

l = 29

Sn = 150

$sn = \frac{n}{2} (a + l)$

$150 = \frac{n}{2} ( - 4 + 29)$

$= \frac{150 \times 2}{25} = n \\ n = 12$

$\frac{12}{2} (2 \times - 4 \: + \: (12 - 1)d )= 150 \\ \\ 6( - 8 + 11d) = 150 \\ \\ - 48 + 66d \: = 150 \\ \\ 66d \: = 150 + 48 \\ \\ d = \frac{198}{66} \\ \\ d = 3$

HENCE , Common difference = 6