Question

the sum of n terms of an AP is n² - n, then It's first term is?​

Answer 1

Answer:

this is the answer

Step-by-step explanation:

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Answer 2

Answer:

The sum of first n terms of an AP is (n² - n) then first term of AP is 0.

Step-by-step explanation:

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

So,

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

On substituting n = 1, we get

$\sf \: S_1 = {1}^{2} - 1$

$\sf \: S_1 = 1 - 1$

$\sf \: S_1 = 0$

$\implies\sf \: \sf \:T_1 = S_1 = 0$

Hence, The sum of first n terms of an AP is (n² - n) then first term of AP is 0.

$\rule{190pt}{2pt}$

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.