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We have a 17 = a + 16d and a 10 = a + 9d According to the given question, a 17 – a 10 = 7 ⇒ (a + 16d) – (a + 9d) = 7 ⇒ a + 16d – a – 9d = 7 ⇒ 7d – 7 ⇒ d = 1 Hence, common difference is 1

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Arithmetic Progressions

Short Answer Type

341. The 17th term of an A .P. exceeds the 10th term by 7. Find the common difference.

We have
a₁₇ = a + 16d
and a₁₀ = a + 9d
According to the given question,
a₁₇ – a₁₀ = 7
⇒ (a + 16d) – (a + 9d) = 7
⇒ a + 16d – a – 9d = 7
⇒ 7d – 7
⇒ d = 1
Hence, common difference is 1

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