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Question
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
Solution
Here, a = 5, d = 3, an = 80
Let the number of terms be n.
Then, we have:
\[a_n = a + \left( n - 1 \right)d\]
\[ \Rightarrow 80 = 5 + \left( n - 1 \right)3\]
\[ \Rightarrow 75 = \left( n - 1 \right)3\]
\[ \Rightarrow 25 = \left( n - 1 \right)\]
\[ \Rightarrow 26 = n\]
Thus, there are 26 terms in the given A.P.
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