First slide

Arithmetic progression

Question

The number of terms common to two A.P.s 3, 7, 11, …, 407 and 2, 9, 16, …, 709 is

Moderate

A

21
B

28
C

14
D

None of these

Solution

By inspection, first common term to both the series is 23. Second common term = 51.
Third = 79 and so on. These numbers form an A.P. 23, 51, 79, …
Since $T_{15} = 23 + 14 (28) = 23 + 392 = 415 > 407$
And $T_{14} = 23 + 13 (28) = 387 < 407$
$∴$ number of common terms = 14.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App