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Determine the general term of an A.P. whose 7th term is –1 and 16th term 17 - Mathematics

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Sum

Determine the general term of an A.P. whose 7th term is –1 and 16th term 17

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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 a7 = – 1 and a16 = 17

a + (7 – 1) d = – 1 and, a + (16 – 1) d = 17

⇒ a + 6d = – 1 ….(i) and, a + 15d = 17 ….(ii)

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

9d = 18 ⇒ d = 2

Putting d = 2 in equation (i), we get

a + 12 = – 1 ⇒ a = – 13

Now, General term = an

= a + (n – 1) d = – 13 + (n – 1) × 2 = 2n – 15

Concept: Arithmetic Progression
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