Question

How do I find the sum of the arithmetic sequence 3, 5, 7, 9, ..., 21?

Answer 1

`120`

Explanation:

Given arithmetic sequence

`3, 5, 7, 9, ........., 21`

The first term `a=3` & a common difference `d=5-3=7-5=\cdots=2`

If there are `n` number of terms in the above A.P. then last term `l=21` will be the nth term given as

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

`21=3+(n-1)2`

`n=10`

hence the sum of given arithmetic progression (`A.P.`) up to `10` terms is given general formula

`S_n=\frac{n}{2}(a+l)`

`S_10=\frac{10}{2}(3+21)`

`=120`

Answer 2

`S_(10)=120`

Explanation:

`"the sum to n terms of an arithmetic sequence is"`

`•color(white)(x)S_n=n/2[2a+(n-1)d]`

`"where a is the first term and d the common difference"`

`"here "a=3,d=7-5=5-3=2,n=10`

`S_(10)=5[(2xx3)+(2xx9)]`

`color(white)(xx)=5(6+18)=120`