The sum of all the terms of a finite A.P. hav | vedclass

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

Question

(A) For a finite Arithmetic Progression $(A.P.)$ with $n$ terms,let $a$ be the first term and $l$ be the last term (also denoted as $a_{n}$). The sum

Vedclass · Accepted Answer

$\frac{1}{2} n(a+l)$

Vedclass · Answer

(A) For a finite Arithmetic Progression $(A.P.)$ with $n$ terms,let $a$ be the first term and $l$ be the last term (also denoted as $a_{n}$). The sum of $n$ terms of an $A.P.$ is given by the formula: $S_{n} = \frac{n}{2} [2a + (n-1)d]$ Since the last term $l = a + (n-1)d$,we can substitute this into the sum formula: $S_{n} = \frac{n}{2} [a + a + (n-1)d]$ $S_{n} = \frac{n}{2} [a + l]$ Thus,the correct expression is $\frac{1}{2} n(a+l)$.

Column $A$	Column $B$
$(A_{1}) \quad 2, -2, -6, -10, \ldots$	$(B_{1}) \quad \frac{2}{3}$
$(A_{2}) \quad a = -18, n = 10, a_{n} = 0$	$(B_{2}) \quad -5$
$(A_{3}) \quad a = 0, a_{10} = 6$	$(B_{3}) \quad 4$
$(A_{4}) \quad a_{2} = 13, a_{4} = 3$	$(B_{4}) \quad -4$
	$(B_{5}) \quad 2$
	$(B_{6}) \quad \frac{1}{2}$
	$(B_{7}) \quad 5$

The sum of all the terms of a finite $A.P.$ having $n$ terms is given by $S_{n} = \ldots \ldots \ldots$

Similar Questions

The $15^{th}$ term of the $A.P.$ $1, 11, 21, 31, \dots$ is........

For the $A.P.$ $4, 8, 12, 16, \ldots$,$T_{40} - T_{30} = \ldots$

The $n^{th}$ term of an $A.P.$ is given by $T_n = 5n - 2$. Then,the $12^{th}$ term of the $A.P.$ is:

The sum of three numbers in $A.P.$ is $-3$ and their product is $8$. Find those numbers.

Vedclass Test Series

Exam Paper Generator

Online Exam Module