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

Options

A. 14
B. 21
C. 28
D. 35

Answer

A

Explanation

Sequence `3,7,11,"…,"407` has commin difference =4 and sequence `2,9,16,"…..,"709` has common difference =7.
Hence, the sequence with common terms has common difference LCM of 4and 7 which is 28.
The first common term is 23.
Hence, the sequence is `23, 51,79,"....,"387` which has 14 terms.
Aliter By inspection, first common term to both the series is 23, second common term in 51, third common term is 79 and so on. These numbers form an AP`23,51,79,"..."`
Since, `T_(14)=23+13(28)=387lt407`
and `T_(15)=23+14(28)=415gt407`
Hence, number of common terms =14