Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

For what value of n, the $n^{th}$ term of the following two A.P's the same.

13, 19, 25, ... and 69, 68, 67, ...

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

answer is D.

(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 two A.P.’s as 13, 19, 25, ... and 69, 68, 67, ...
We know, the formula of

n^{th}

term is,

T n = a + n − 1 d

.
The first term is a.
The common difference is d.
The number of terms are n.
Therefore, according to the first A.P.,

T n = 13 + n − 1 6 ⇒ T n = 13 + 6 n − 6 ⇒ T n = 6 n + 7

The

n^{th}

term of 1st A.P is

T n = 6 n + 7...... 1

.
Again, for the second A.P.,

T n = 69 + n − 1 − 1 ⇒ T n = 69 − n + 1 ⇒ T n = 70 − n

The nth term of A.P is

T n = 70 − n ...... (2)

Equating equations (1) and (2),

6 n + 7 = 70 − n ⇒ 6 n + n = 70 − 7 ⇒ 7 n = 63 ⇒ n = 9

The 9th term is a common term to both series 13,19,25,....... and 69,68,67,........
Therefore, option 4 is correct.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE