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

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, then how many terms are there and what is their sum?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

n = 40 S 40 = 6950

n = 45 S 45 = 7000

n = 38

S 38 = 6973

n = 30 S 30 = 5500

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given:

a = 17, l = 350 and d = 9

.
Let there are n terms in the A.P.
Formula for the

n t h

term:

a n = a + n − 1 × d

Applying nth term of an A.P. formula:

∴ a n = l = 350 ⇒ 17 + (n − 1) × 9 = 350 ⇒ 9 n + 8 = 350 ⇒ 9 n = 350 − 8

⇒ 9 n = 342 ⇒ n = 3429 ⇒ n = 38

Thus, there are 38 terms in the A.P.
Formula used for sum of first term of A.P.:

S n = n 2 [a + l]

Applying sum of 38 terms of an A.P. formula:

∴ S 38 = 382 (17 + 350) ⇒ S 38 = 19 × 367 = 6973

Therefore, are there 38 terms and the required sum is 6973.
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 Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

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!