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

The number of terms common to the two A.P.s 3, 7, 11,... | 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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