Math, asked by kartikaykapoor88, 9 months ago

The sum of first n terms of an AP is (2n² - n) then 2nd term of AP will be *​

Answers

Answered by mathdude500
2

Answer:

The sum of first n terms of an AP is (2n² - n) then 2nd term of AP will be 5

Step-by-step explanation:

Given that, sum of first n terms of an AP is 2n² - n.

So,

\sf \: S_n =  {2n}^{2} - n \\  \\

We know,

\sf \: T_n = S_n - S_{n - 1} \\  \\

So, on substituting n = 2, we get

\sf \: T_2 = S_2 - S_{1} \\  \\

\sf \: T_2 = [ 2 {(2)}^{2} - 2] - [ 2 {(1)}^{2} - 1] \\  \\

\sf \: T_2 = (8 - 2) - (2 - 1) \\  \\

\sf \: T_2 = 6 - 1 \\  \\

\implies\sf \: \sf \: T_2 = 5 \\  \\

Hence, The sum of first n terms of an AP is (2n² - n) then 2nd term of AP will be 5

\rule{190pt}{2pt}

Additional Information

↝ nᵗʰ term of an arithmetic progression is,

\begin{gathered}\bigstar\:\:{\underline{{\boxed{\sf{{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}

↝ Sum of n  terms of an arithmetic progression is,

\begin{gathered}\bigstar\:\:{\underline{{\boxed{\sf{{S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}

Wʜᴇʀᴇ,

a is the first term of the progression.

n is the no. of terms.

d is the common difference.

Similar questions