Question

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

• A. 14
• B. 21
• C. 28
• D. none of these

Answer 1

Answer: (A)

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