If the nth term of an AP is 2 n+1, find the sum of first n terms of the AP
Home
/
If the nth term of an AP is 2 n+1, find the sum of first n terms of the AP
If the nth term of an AP is 2 n+1, find the sum of first n terms of the AP
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer :
➥ The sum of first n terms of the AP = n² + 2n
Given :
➤ aₙ = 2n + 1
To Find :
➤ Sum of first n terms of the AP = ?
Solution :
◈ a₁ = (2 × 1 + 1) = 3
◈ a₂ = (2 × 2 + 1) = 5
∴ a = 3
⟾ d = a₁ - a₂
⟾ d = 5 - 3
⟾ d = 2
Now ,
[tex] \tt{: \implies s_{n} = \dfrac{n}{2} \left\{ 2a + (n - 1)d \right \}}[/tex]
[tex] \tt{: \implies s_{n} = \dfrac{n}{2} \{ 2 \times 3(n - 1) \times 2\} }[/tex]
[tex] \tt{: \implies s_{n} = \dfrac{n}{2}(6 + 2n - 2) }[/tex]
[tex] \tt{: \implies s_{n} = \dfrac{n}{2} (6 - 2 + 2n)}[/tex]
[tex] \tt{: \implies s_{n} = \dfrac{n}{2} (4 + 2n)}[/tex]
[tex] \tt{: \implies s_{n} = n(n + 2)}[/tex]
[tex] \bf{: \implies \underline{ \: \: \underline{ \purple{ \: \: s_{n} = {n}^{2} + 2n \: \: }} \: \: }}[/tex]
Hence, the sum of first n terms of the AP is n² + 2n.