Question

in an AP the first term is -4 and last term is 29 and the sum of the term is 150 find the common difference ?​

Answer 1

Answer:

Step-by-step explanation:

Given :

In an AP, the first term is - 4,

and last term is 29,

and the sum of all the terms is 150,

find the common difference.

Solution :

We know that,

The formula for $S_n$ is also given by,

⇒ $S_n = \frac{n}{2}(a + l)$

Here,

n = no. of terms

a = first term,

l = last term,.

By substituting,

a = -4,

l = 29,

$S_n$ = 150

We get,.

⇒ $150=\frac{n}{2}(-4+29)$

⇒ $150 = \frac{n}{2} (25)$

⇒ $150 \times 2 = n \times (25)$

⇒ $300 = 25n$

⇒ $n = \frac{300}{25} = 12$

⇒ n = 12,.

We know that,

⇒ $a_n = a + (n - 1)d$

By substituting,

$a_n$ = 29,

a = -4

n = 12

We get,

⇒ $29 = -4 + (12 - 1) d$

⇒ $29 + 4 = 11d$

⇒ $33 = 11d$

⇒ $d = \frac{33}{11} = 3$