Question

Find S25 for 1/2 + 1 + 3/2 + 2 + ...

Answer 1

`S_(25)=(325)/(2)`

Explanation:

The given sequence:

`(1)/(2)+1+(3)/(2)+2+ ...`

Here, first term (a) =
`(1)/(2)`, common difference(d) =
`1-(1)/(2)=(1)/(2)` and

the number of terms (n) = 25

The given sequence are in AP.

To find, the value of
`S_(25)` = ?

We know that,

The sum of nth terms of an AP

`S_(n)=(n)/(2)[2a+(n-1)d]`

The sum of 25th terms of an AP

`S_(25)=(25)/(2)[2((1)/(2))+(25-1)((1)/(2))]`

⇒
`S_(25)=(25)/(2)[1+(24)((1)/(2))]`

⇒
`S_(25)=(25)/(2)[1+12]`

⇒
`S_(25)=(25)/(2)[13]`

⇒
`S_(25)=(325)/(2)`

∴
`S_(25)=(325)/(2)`