Question

Find a formula for the n th term, T n , of an arithmetic sequence where the 2nd term is 7 and the 6th term is 27.

Answer 1

Given:

a2 = 7

a6 = 27

To find:

nth term of the A.P.

Solution:

A.T.Q.

a2 = 7

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

Where a is the first term of the A.P.

d is the common difference

and, n is the place of the no. in an A.P.

=> a+(2-1)d = 7

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

Also, a6 = 27

=> a+5d = 27

Now, from (1) We get,

a = 7-d --------------(2)

Putting the value of a in the above equation

We get, (7-d)+5d = 27

=> 7-d+5d = 27

=> 7+4d = 27

=> 4d = 27-7

=> 4d = 20

=> d = 20/4

=> d = 5

Now, putting the value of d in equation (2)

We get, a = 7-5

=> a = 2

Hence, The A.P. so formed is as follows:

2, 2+5, 2+5(2), 2+5(3) ..........

=> A.P. = 2, 7, 12, 17..........

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