Question

The number of common terms to the two sequences 17, 21, 25 .......... 417 and 16, 21, 26 ....... 466 is

• A. 21
• B. 19
• C. 20
• D. 91

Answer 1

The correct option is C

20

The common difference of 1st A.P=4
The common difference of 2nd A.P=5
First common term is 21
The terms common to both the A.P will form another A.P with first term 21 and common difference 20[L.C.M of 5 and 4] So the A.P will be
21, 22 + 20, 21 + 2 x 20 ..... 21 + (n-1)20
The last term of this A.P will be less than or equal to 417, the least of the last terms of two given A.Ps
21 + (n-1)20 $\le$ 417
$\Rightarrow$(n-1)20 $\le$ 396
(n-1) $\le$ 19
n $\le$ 20
$\Rightarrow$ Number of terms is 20 and the last term will be 21 + 19 x 20 =401