The sum of all those terms of the arithmetic | vedclass

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

Question

(D) The given arithmetic progression is $3, 8, 13, \ldots, 373$.Here,$a = 3$,$d = 5$. The $n$-th term is $a_n = a + (n-1)d = 3 + (n-1)5 = 373$.$5(n-1)

Vedclass · Accepted Answer

$9525$

Vedclass · Answer

(D) The given arithmetic progression is $3, 8, 13, \ldots, 373$.Here,$a = 3$,$d = 5$. The $n$-th term is $a_n = a + (n-1)d = 3 + (n-1)5 = 373$.$5(n-1) = 370 \implies n-1 = 74 \implies n = 75$.The total sum $S_{75} = \frac{75}{2}(3 + 373) = \frac{75}{2}(376) = 75 	imes 188 = 14100$.Terms divisible by $3$ are of the form $3 + (k-1)5$ such that $3 + 5k - 5$ is a multiple of $3$,i.e.,$5k - 2 = 3m \implies 5k \equiv 2 \pmod 3 \implies 2k \equiv 2 \pmod 3 \implies k \equiv 1 \pmod 3$.So $k = 1, 4, 7, \ldots$. The terms are $3, 18, 33, \ldots$.The last term is $363$ (since $363 = 3 + (m-1)15 \implies 360 = (m-1)15 \implies m-1 = 24 \implies m = 25$).Sum of terms divisible by $3$ is $S' = \frac{25}{2}(3 + 363) = \frac{25}{2}(366) = 25 	imes 183 = 4575$.Required sum $= 14100 - 4575 = 9525$.

The sum of all those terms of the arithmetic progression $3, 8, 13, \ldots, 373$ which are not divisible by $3$ is equal to $.......$.

Similar Questions

The sum of three terms of an Arithmetic Progression $(AP)$ is $18$ and the sum of their squares is $158$. The largest term is.......

If $\log _{3} 2, \log _{3}(2^{x}-5), \log _{3}(2^{x}-\frac{7}{2})$ are in an arithmetic progression,then the value of $x$ is equal to $.....$

The sum of $1 + 3 + 5 + 7 + \dots$ up to $n$ terms is

$A$ man starts repaying a loan with a first installment of $Rs. 100$. If he increases the installment by $Rs. 5$ every month,what amount will he pay in the $30^{th}$ installment?

Suppose that all the terms of an arithmetic progression $(A.P.)$ are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is $6:11$ and the seventh term lies between $130$ and $140$,then the common difference of this $A.P.$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module