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Answer :

\( a_{17} = a_{10} + 7\)

Using formula \(a_n = a + (n - 1)d\), to find nth term of arithmetic progression,

\(a_{17}\) = a + 16d… (2)

\(a_{10}\) = a + 9d… (3)

Putting (2) and (3) in equation (1),

a + 16d = a + 9d + 7

\(\Rightarrow \) 7d = 7

\(\Rightarrow \) d = 1

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- An AP consists of 50 terms of which \(3^{rd}\) term is 12 and the last term is 106. Find the \(29^{th}\) term.
- If the \(3^{rd}\) and the \(9^{th}\) terms of an AP are 4 and –8 respectively, which term of this AP is zero?
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- The sum of the \(4^{th}\) and \(8^{th}\) terms of an AP is 24 and the sum of \(6^{th}\) and \(10^{th}\) terms is 44. Find the three terms of the AP.
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