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# 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.

Video Solution
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 $$1.$$

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