Question

Find the indicated terms in each of the following sequences whose nth terms are:

`a_n = (3n - 2)/(4n + 5)`; `a_7 and a_8`

Answer 1

Here, we are given the n^th term for various sequences. We need to find the indicated terms of the A.P.

`a_n = (3n - 2)/(4n + 5)`

We need to find `a_7` and `a_8`

Now to find `a_7` term we use n = 7 we get

`a_7 = (3(7) - 2)/(4(7) + 5)`

`= (21 -2)/(28 + 5)`

`= 19/33`

Also to find `a_8` term we use n = 8 we get

`a_8 = (3(8) -2)/(4(8) + 5)`

`= (24 - 2)/(32 + 5)`

`= 22/37`

Thus `a_7 = 19/33` and `a_8 = 22/37`