Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

The 16th term of an AP is 5 times its 3rd term. If its 10th term is 41, then what is the sum of its first 15 terms?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

400

495

450

500

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given that, 16th term of an AP is 5 times its 3rd term and 10th tern is 41.
Formula used for nth term of A.P.:

t n = a + n − 1 d

Formula used for sum of first n term of A.P.:

S n = n 2 [2 a + (n − 1) d]

Let the first term be a and the common difference be d.

∵ t 16 = 5 × t 3 − − − − (1) And t 3 = a + (3 − 1) d ⇒ t 3 = a + 2 d

Applying the formula of nth term of A.P. in 16th term:

t 16 = a + (16 − 1) d t 16 = a + 15 d

∴ a + 15 d = 5 (a + 2 d) [from 1] ⇒ a + 15 d = 5 a + 10 d ⇒ 4 a = 5 d − − − (2)

We have,

t 10 = 10

Applying the formula of nth term of A.P. in 10th term:

\Rightarrow t_{10} = a + (10 - 1) d

\Rightarrow t_{10} = a + 9 d

∴ a + 9 d = 41 ⇒ a = 41 − 9 d − − − − (3)

Put the value of a in equation (2):

∴ 4 (41 − 9 d) = 5 d ⇒ 164 − 36 d = 5 d ⇒ 41 d = 164 ⇒ d = 4

Put the value of d = 4 in equation (3):

∴ a = 41 − 9 × 4 ⇒ a = 41 − 36 = 5

Since,

S n = n 2 [2 a + (n − 1) d]

∴ S 15 = 152 [2 × 5 + (15 − 1) 4] ⇒ S 15 = 152 × (10 + 56) = 152 × 66 = 495

Therefore, the sum of its first 15 terms is 495.
Hence, option (2) is correct.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE