Question

Write an equation for the n

th term of the arithmetic seqeuence. Then find a10
a
10
.

1/2,1,11/2,2

Answer 1

Given:

The arithmetic sequence is

`(1)/(2),1,1(1)/(2),2`

To find:

The nth term of the given arithmetic sequence and then find
`a_(10)`.

Solution:

We have,

`(1)/(2),1,1(1)/(2),2`

Here,

First term:
`a=(1)/(2)`

Common difference:
`d=1-(1)/(2)=(1)/(2)`

nth term of an arithmetic sequence is

`a_n=a+(n-1)d`

where, a is first term and d is common difference.

`a_n=(1)/(2)+(n-1)(1)/(2)`

`a_n=(1)/(2)+(1)/(2)n-(1)/(2)`

`a_n=(1)/(2)n`

Now, put n=10, to find
`a_(10)`.

`a_(10)=(1)/(2)(10)`

`a_(10)=5`

Therefore, the nth term of the given arithmetic sequence is
`a_n=(1)/(2)n` and the value of
`a_(10)` is 5.