Find the sum of the first n terms of the A.P. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given $A.P.$ is $5, 2, -1, \ldots$Here,the first term $a = 5$.The common difference $d = 2 - 5 = -3$.The sum of the first $n$ terms of an $A.P

Vedclass · Accepted Answer

$S_n = -\frac{3}{2}n^2 + \frac{13}{2}n$

Vedclass · Answer

(A) The given $A.P.$ is $5, 2, -1, \ldots$Here,the first term $a = 5$.The common difference $d = 2 - 5 = -3$.The sum of the first $n$ terms of an $A.P.$ is given by the formula $S_n = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values of $a$ and $d$:$S_n = \frac{n}{2}[2(5) + (n - 1)(-3)]$$S_n = \frac{n}{2}[10 - 3n + 3]$$S_n = \frac{n}{2}[13 - 3n]$$S_n = \frac{13n}{2} - \frac{3n^2}{2}$Thus,$S_n = -\frac{3}{2}n^2 + \frac{13}{2}n$.

Find the sum of the first $n$ terms of the $A.P.$ $5, 2, -1, \ldots$

Similar Questions

The first term of an $A.P.$ is denoted by $\ldots \ldots \ldots \ldots .$

If $a=2$ and $d=4,$ then $S_{40}=\ldots \ldots \ldots$

For an $A.P.$,the first term is $10$ and the $10^{th}$ term is $100$. Then,the sum of the first $10$ terms is..........

Which term of the $A.P. \, 53, 48, 43, \ldots$ is the first negative term?

The $9^{th}$ term of an $A.P.$ is $0.$ Show that the $29^{th}$ term of the $A.P.$ is two times its $19^{th}$ term.

Vedclass Test Series

Exam Paper Generator

Online Exam Module