Question

Prove that
The first term of an AP is 5, the last term is
45 and the sum & is you find the number
400. of
terms and the common difference.​

Answer 1

Given

•First term (a) = 5

• Last term = 45

• Sn = 400

★ To find ★

•Common difference

• Terms

✬ Solution ✬

Sn = $\frac{n}{2}$ (a+1)

⇒400 = $\frac{n}{2}$ (5+45)

⇒400 = $\frac{n}{2}$ (50)

⇒400 = n×25

⇒ n = 15

Now ,

l=a+(n−1)d

⇒45=5+(16−1)d

⇒45−5=(15)d

⇒40=15d

⇒ d = $\frac{40}{15}$

⇒d = $\frac{8}{3}$

So, The common difference = $\frac{8}{3}$