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Question
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
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Solution
Given
\[a = 7, n = 60, l = 125\]
\[l = a + (n - 1)d\]
\[ \Rightarrow 125 = 7 + (60 - 1)d\]
\[ \Rightarrow 125 = 7 + 59d\]
\[ \Rightarrow 118 = 59d\]
\[ \Rightarrow 2 = d\]
\[a_{32} = a + \left( 32 - 1 \right)d\]
\[ = a + 31d \]
\[ = 7 + 31 \times 2 \]
\[ = 7 + 62 \]
\[ = 69\]
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