The sum of the first 30 positive multiples of | vedclass

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

Question

(D) The first $30$ positive multiples of $6$ form an Arithmetic Progression $(A.P.)$ where the first term $a = 6$ and the common difference $d = 6$.Th

Vedclass · Accepted Answer

$2790$

Vedclass · Answer

(D) The first $30$ positive multiples of $6$ form an Arithmetic Progression $(A.P.)$ where the first term $a = 6$ and the common difference $d = 6$.The $30^{th}$ term (last term) is $l = 6 	imes 30 = 180$.The sum of $n$ terms of an $A.P.$ is given by the formula $S_n = \frac{n}{2}(a + l)$.Substituting the values $n = 30$,$a = 6$,and $l = 180$:$S_{30} = \frac{30}{2}(6 + 180)$$S_{30} = 15 	imes 186$$S_{30} = 2790$.

The sum of the first $30$ positive multiples of $6$ is:

Similar Questions

Find the $100^{th}$ term of the $A.P.$ $50, 56, 62, 68, \ldots$

In an $AP$,if $S_{n} = 3n^{2} + 5n$ and $a_{k} = 164$,find the value of $k$.

For an $A.P.$,the first term is $10$,the $n^{th}$ term is $40$,and the sum of the first $n$ terms is $150$. Find the value of $n$ and the common difference $d$.

In each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a = \frac{15}{2}, \quad d = \frac{3}{2}$

If the common difference of an $AP$ is $5,$ then what is $a_{18}-a_{13} ?$

Vedclass Test Series

Exam Paper Generator

Online Exam Module