Question

The 7th term of an ap is -1 and its 16 th term is 17 .what is the nth term of the ap

Answer 1

Answer:

nth term = 9n/5 - 68/5

Step-by-step explanation:

Let the first term of ap = a

   common difference = d

7th term = -1

a + (7 - 1) d = -1

a + 6d = -1   .......(1)

16th term = 17

a + (17 - 1) d = 17

a + 16d = 17    ........(2)

From 1 and 2 we get,

a = -59/5 and d = 9/5

nth term = -59/5 + (n-1) 9/5

               = 9n/5 - 68/5

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Answer 2

Answer:

a = -13 ; d = 2 ; nth term of A.P. = a+(n-1)d

= -13+(n-1)2

Step-by-step explanation:

(a+6d) = -1. ------ 1

(a+15d) = 17 ----- 2

[ 'a' is the first term of given A.P. and 'd' is the common difference b/w the terms of given A. P.]

From equations 1 and 2 : (subtract 2 from 1)

a+6d = -1

-a-15d = -17

-9d = -18

d = -18

-9

d = 2

Substitute the value of d in any of the equations,

a+6(2) = -1

a+12= -1

a = -1-12

a = -13