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Q.
The number of terms common to two A.P.'s $3, 7, 11,..........., 407$ and $ 2, 9, 16,............,709$ is
Sequences and Series
Solution:
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 $= 14$.