Question

Determine the nth term of the ap whose 7th term is -4 and 16th term is 17​ 1

Answer 1

Step-by-step explanation:

In AP, nth term = a + (n - 1)d, where a is first term and d is common difference.

Let the first term of this AP be a and common difference be d.

According to question:

= > 7th term = - 4

= > a + (7 - 1)d = - 4

= > a + 6d = - 4

= > a = - 4 - 6d

= > 16th term = 17

= > a + (16 - 1)d = 17

= > a + 15d = 17

= > - 4 - 6d + 15d = 17 { a = - 4 - 6d }

= > 9d = 17 + 4

= > 9d = 21

= > d = 7/3

Therefore, a = - 4 - 6(7/3) = - 4 - 14 = - 18

Thus,

= > nth term = - 18 + (n - 1)(7/3) = (1/3){-54 + 7n - 7} = (1/3){ 7n - 61 }

= > nth term = 3 - n

Answer 2

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