Trying to find the right answer to this..

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

41.

Find the number of terms in each of the following APs :

$space space space 18 comma space 15 1 half comma space 13 comma space....... comma space minus 47$

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42.

Check whether – 150 is a term of the AP : 11, 8, 5, 2 . .

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43.

Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

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44.

An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

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45. If the 3rd and 9th terms of an A .P. are 4 and -8 respectively, which term is zero?

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46. 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.