Question

in an ap first term is -4 the last term is 29 and the sum of all its terms is 150. Find its common difference

Answer 1

25 and 121 is the answer

Answer 2

Answer:

The Common Difference is 3.

Step-by-step explanation:

Given: First term, a = -4

           last term, l = 29

           Sum of all term is 150

Let d be the common difference.

According to question,

$a_n=a+(n-1)d$

$29=-4+(n-1)d$

$(n-1)d=33$ ..................(1)

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

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

$300=25n$

$n=\frac{300}{25}$

$n=12$

putting this value in (1) we get,

( 12 - 1 ) d = 33

11d = 33

d = 3

Therefore, The Common Difference is 3.