The sum of integers from 1 to 50 that are div | vedclass

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

Question

(B) Integers divisible by both $2$ and $3$ are divisible by their least common multiple,which is $6$. The integers from $1$ to $50$ divisible by $6$ a

Vedclass · Accepted Answer

$6^3$

Vedclass · Answer

(B) Integers divisible by both $2$ and $3$ are divisible by their least common multiple,which is $6$. The integers from $1$ to $50$ divisible by $6$ are $6, 12, 18, \dots, 48$. This forms an Arithmetic Progression $(AP)$ where the first term $a = 6$,the last term $a_n = 48$,and the common difference $d = 6$. Using the formula $a_n = a + (n - 1)d$: $48 = 6 + (n - 1)6$ $42 = (n - 1)6$ $n - 1 = 7 \Rightarrow n = 8$. The sum $S_n$ of an $AP$ is given by $S_n = \frac{n}{2}(a + a_n)$: $S_8 = \frac{8}{2}(6 + 48) = 4(54) = 216$. Since $216 = 6^3$,the correct option is $B$.

The sum of integers from $1$ to $50$ that are divisible by both $2$ and $3$ is

Similar Questions

The common difference of the $A.P.$ $b_{1}, b_{2}, \ldots, b_{m}$ is $2$ more than the common difference of $A.P.$ $a_{1}, a_{2}, \ldots, a_{n}$. If $a_{40} = -159$,$a_{100} = -399$ and $b_{100} = a_{70}$,then $b_{1}$ is equal to:

If $x, y, z$ are in an arithmetic progression,and $a$ is the arithmetic mean of $x$ and $y$,and $b$ is the arithmetic mean of $y$ and $z$,then what is the arithmetic mean of $a$ and $b$?

$2+3+5+6+8+9+\ldots$ to $2n$ terms $=$

Jairam purchased a house for Rs. $15000$ and paid Rs. $5000$ at once. He promised to pay the remaining amount in annual installments of Rs. $1000$ with $10\%$ per annum interest on the outstanding balance. How much total money will be paid by Jairam in Rs.?

If the sum of the first $n$ terms of an arithmetic progression is $cn^2$,what is the sum of the squares of these $n$ terms?

Vedclass Test Series

Exam Paper Generator

Online Exam Module