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Question
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
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Solution
7, 10, 13...43 Here, we have:
a = 7
\[d = (10 - 7) = 3\]
\[ a_n = 43\]
Let there be n terms in the given A.P.
\[\text { Also }, a_n = a + \left( n - 1 \right)d\]
\[ \Rightarrow 43 = 7 + \left( n - 1 \right)3\]
\[ \Rightarrow 36 = \left( n - 1 \right)3\]
\[ \Rightarrow 12 = \left( n - 1 \right)\]
\[ \Rightarrow 13 = n\]
Thus, there are 13 terms in the given A.P.
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