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

9525 Explanation: Given A.P. is Using , we get: Sum of complete A.P. = Now, the numbers divisible by 3 are Using , we get: So sum of this A.P. = Hence, the required sum is

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JEE 2023 Mathematics PYQ — The sum of all those terms, of the arithmetic progression 3, 8, 1… | Mathem Solvex

A.
9525
(Correct Answer)
B.
9552
C.
9558
D.
9585

Correct Answer:

9525

Explanation

Given A.P. is $3, 8, 13, \dots, 373$

Using

T_n = a + (n - 1)d

, we get:

373 = 3 + (n - 1) 5 \implies n = 75

Sum of complete A.P. =

\frac{n}{2}(a + l) = \frac{75}{2}(3 + 373) = 14100

Now, the numbers divisible by 3 are $3, 18, 33, \dots, 363$

Using

T_k = a + (k - 1)d

, we get:

363 = 3 + (k - 1) 15 \implies k = 25

So sum of this A.P. =

\frac{k}{2}(a + l) = \frac{25}{2}(3 + 363) = 4575

Hence, the required sum is

14100 - 4575 = 9525

JEE 2023 — Mathematics PYQ

Choose the correct answer:

Explanation

Explanation