AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

What is the sum of the first 51 terms of an AP whose second and third terms are 14 and 18 respectively?

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

5610

5550

5500

5000

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given that the second and third term are 14 and 18 respectively.
Let the first term be a and the common difference be d.
Determining common difference:

∴ d = a 3 − a 2 ⇒ d = 18 − 14 ⇒ d = 4

Formula used for nth term of A.P.:

a n = a + n − 1 d

Determining first term:

∴ a n = a + (n − 1) d ⇒ a 2 = a + (2 − 1) 4 ⇒ 14 = a + 4 ⇒ a = 14 − 4 ⇒ a = 10

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

S n = n 2 [2 a + (n − 1) d]

Determining the sum of 51 terms:

∴ S 51 = 512 [2 × 10 + (51 − 1) 4] ⇒ S 51 = 512 [20 + (50) 4] = 512 [20 + 200] = 512 [220]

⇒ S 51 = 5610

Therefore, the sum of 51 terms is 5610.
Hence, option (1) is correct.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Ready to Test Your Skills?

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

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th