Ex.5.2 Q10 Arithmetic Progressions Solution - NCERT Maths Class 10

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Question

The \(17^\rm{th}\) term of an AP exceeds its \(10^\rm{th}\) term by \(7.\) Find the common difference.

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Arithmetic Progressions
Ex 5.2 | Question 10

Text Solution

What is Known:?

The difference between the \(17^\rm{th}\) and \(10^\rm{th}\) term.

What is Unknown?

Common difference \(d\)

Reasoning:

\({a_n} = a + \left( {n - 1} \right)d\) is the general term of AP. Where \({a_n}\) is the \(n\rm{th}\) term, \(a\) is the first term, \(d\) is the common difference and \(n\) is the number of terms.

Steps:

\[\begin{align}{a_{17}} &= a + (17 - 1)d\\{a_{17}} &= a + 16d\\\\{a_{10}} &= a + (10 - 1)d\\{a_{10}} &= a + 9d\\\\{a_{17}} - {a_{10}} &= 7\\16d - 9d& = 7\\d &= 1\end{align}\]

The common difference is \(1.\)