Find the sum of the first 40 positive integer | vedclass

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

Question

(A) The positive integers that are divisible by $6$ are $6, 12, 18, 24, \ldots$This sequence forms an Arithmetic Progression $(A.P.)$ where the first

Vedclass · Accepted Answer

$4920$

Vedclass · Answer

(A) The positive integers that are divisible by $6$ are $6, 12, 18, 24, \ldots$This sequence forms an Arithmetic Progression $(A.P.)$ where the first term $a = 6$ and the common difference $d = 6$.We need to find the sum of the first $n = 40$ terms.The formula for the sum of the first $n$ terms of an $A.P.$ is $S_n = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values $n = 40$,$a = 6$,and $d = 6$:$S_{40} = \frac{40}{2}[2(6) + (40 - 1)6]$$S_{40} = 20[12 + (39)(6)]$$S_{40} = 20[12 + 234]$$S_{40} = 20 	imes 246$$S_{40} = 4920$.

Find the sum of the first $40$ positive integers divisible by $6$.

Similar Questions

For the following $APs$,write the first term and the common difference: $\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, \ldots$

The sum of the $4^{th}$ and $8^{th}$ terms of an $AP$ is $24$ and the sum of the $6^{th}$ and $10^{th}$ terms is $44$. Find the first three terms of the $AP$.

Find the sum of the following $APs$ $-37, -33, -29, \ldots$ to $12$ terms.

For the $AP: \frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots,$ write the first term $a$ and the common difference $d$.

How many terms of the $AP: 24, 21, 18, \ldots$ must be taken so that their sum is $78$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module