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

State True/False.

If the sum of the first 14 terms of an AP is 1505 and the first term of an AP is 10, then 25th term is 370.

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

True

False

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 sum of 14 term is 1505.

⇒ S 14 = 1505

Let the first term be a and common difference be d.
a = 10
Formula used for sum of first n term of A.P.:

S n = n 2 [2 a + (n − 1) d]

Applying formula for sum of first n terms of A.P.:

∴ S 14 = 142 [2 (10) + (14 − 1) d] ⇒ 1505 = 7 [20 + (13) d] ⇒ 215 = 20 + 13 d ⇒ 13 d = 195 ⇒ d = 15

Therefore, the common difference is 15.
Formula for the

n t h

term:

a n = a + n − 1 × d

So, the 25th term of the A.P. is:

∴ a 25 = 10 + (25 − 1) 15 ⇒ a 25 = 10 + (24) 15 = 10 + 360 = 370

Therefore,

25 th term of the A .P . is 370 .

Thus, the given statement is true.
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!