Question

if an=2n+3 nind s1,s2,s3

Answer 1

$\bf\large\bold\green{\underline{\overline{HERE\: IS\: YOUR\: ANSWER}}}$

$\bf\bold\orange{\boxed{MARK\: AS \:BRAINLIEST}}$

Answer 2

Answer :

$\large{\boxed{\bf{\star\:\:S_1\:=\:5\:,\:S_2\:=\:12\:and\:S_3\:=\:21.\:\:\star}}}$

Correct Question :–

If $\sf{a_n\:=\:2n\:+\:3}$ then find S₁ , S₂ , S₃ .

Explanation :

Given :–

• $\sf{a_n\:=\:2n\:+\:3}$

To Find :–

• Values of S₁ , S₂ and S₃

Formula Applied :–

• $\boxed{\bf{\star\:\:S_n\:=\:\dfrac{n}{2} [2a\:+\:(n\:-\:1)d\:\:\star]}}$

• $\boxed{\bf{\star\:\:a_n\:=\:a\:+\:(n\:-\:1)d\:\:\star}}$

• $\boxed{\bf{\star\:\:d \:= \:a_{n+1}\:0-\:a_{n}\:\:\star}}$

Solution :–

We have, aₙ = 2n + 3.

When putting n = 1, we get :

a₁ = 2(1) +3

a = 2 + 3

a = 5

When putting n = 2 , we get :

a₂ = 2(2) + 3

a₂ = 4 + 3

a₂ = 7

Now , we will find common difference (d) :

d = a₍₁₊₁₎ - a₁

d = a₂ - a₁

d = 7 - 5

d = 2

1. We have to find S₁ :

$\sf{S_1\:=\:\dfrac{1}{2}\:[2(5)\:+\:(1\:-\:1)(2) ]}$

$\sf{S_1\:=\:\dfrac{1}{2}\:[10\:+\:(0\:\times\:2)] }$

$\sf{S_1\:=\:\dfrac{1}{2}\:\times\:10 }$

$\boxed{\sf{S_1\:=\:5 }}$

2. We have to find S₂ :

$\sf{S_2\:=\:\dfrac{2}{2}\:[2(5)\:+\:(2\:-\:1)(2)] }$

$\sf{S_2\:=\:[10\:+\:(1\:\times\:2) ]}$

$\sf{S_2\:=\:10\:+\:2}$

$\boxed{\sf{S_2\:=\:12}}$

3. We have to find S₃ :

$\sf{S_3\:=\:\dfrac{3}{2}\:[2(5)\:+\:(3\:-\:1)(2)] }$

$\sf{S_3\:=\:\dfrac{3}{2}\:[10\:+\:(2\:\times\:2)] }$

$\sf{S_3\:=\:\dfrac{3}{2}\:(10\:+\:4) }$

$\sf{S_3\:=\:\dfrac{3}{2}\:\times\:14 }$

$\sf{S_3\:=\:3\:\times\:7 }$

$\boxed{\sf{S_3\:=\:21 }}$

∴ The values of S₁ , S₂ and S₃ are 5 , 12 and 21 Respectively.