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)

14

Answer 2

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