The number of terms common to the two A.P.s 3, 7, 11,..,407 and 2,9,16,..,709 is : Sequence & Series (Mathematics)

Given A.P.'s are

3,7,11, \ldots ., 407

and

2,9,16 . \ldots .709

.\n\nSince, the given, A.P.s have common difference 4 and 7 respectively. So, first common term to both A.P.'s = 23\nNow, common difference of A.P.'s of common terms to given A.P's is L.C.M.

(4,7)=7 \times 4=28

\n\nLast term

\leq 407

\n\begin{aligned}\n& \Rightarrow 23+(n-1) \times 28 \leq 407 \\\n& \Rightarrow(n-1) \times 28 \leq 384 \Rightarrow n \leq 14.71 . \text { So, } n=14\n\end{aligned}\n

Explanation

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