The 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term and the general term - Mathematics

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Sum

The 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term and the general term

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Solution

Let a be the first term and d be the common difference of the given A.P. Let the A.P. be

a1 , a2 , a3 , ….. an, ……

It is given that a10 = 52 and a16 = 82

⇒ a + (10 – 1) d = 52 and a + (16 – 1) d = 82

⇒ a + 9d = 52 ….(i) and, a + 15d = 82 ….(ii)

Subtracting equation (ii) from equation (i), we get

–6d = – 30 ⇒ d = 5

Putting d = 5 in equation (i), we get

a + 45 = 52 ⇒ a = 7

∴ a32 = a + (32 – 1) d = 7 + 31 × 5 = 162

and, an = a + (n – 1) d = 7 (n – 1) × 5 = 5n + 2.

Hence a32 = 162 and an = 5n + 2

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