Question

Calculate s5 for the sequence defined by

Answer 1

42.5 is the one

Answer 2

ANSWER


`S_5= 42.5`

Step-by-step explanation

The general term of the arithmetic sequence is


`a_n=1+(5)/(2)n`

For the first term,we substitute
`n=1` to get,


`a_1=1+(5)/(2)* 1`


`a_1=1+2.5=3.5`

Similarly


`a_5=1+(5)/(2)* 5`


`a_5=13.5`

The sum of the first n-terms is given by the formula,


`S_n=(n)/(2)(a_1+l)`

where l is the last term.
In this case


`l=a_5=13.5`

We substitute these values to get,


`S_5= (5)/(2) (3.5 + 13.5)`


`S_5= (5)/(2) (17)`

`S_5=42.5`



We could have also used the formula,


`S_n=(n)/(2)(2a_1+(n-1)d)`


`S_5=(5)/(2)(2(3.5)+(5-1)2.5)`


`S_5=42.5`