Question

The number of common terms of the progression 4, 9, 14....... up to 25 terms and 3, 6, 9,..... up to 37 terms, is

(1) 8

(2) 9

(3) 7

(4) 10

Answer 1

Correct option is (3) 7

4, 9, 14.....

T₂₅ =  25 x 5 = 125

Common diff =  5

and 3, 6, 9,...

T₃₇ = 37 x 3 = 111

Common diff = 3

Clearly first common term = 9

Common diff L.C.M (5, 3) = 15

\(\therefore\) T_n (of common terms of two given A.P.) = 9 + (n - 1) × 15

= 15n - 6

\(\therefore\) 15n - 6 ≤ 111

15n ≤ 117

n ≤ 7.8

\(\therefore\) Number of common terms = 7