Question

Calculate s50 for the arithmetic sequence defined by

Answer 1

Answer: D. 617.5 hope that helps !

Answer 2

617.5

Explanation:

If you expand the series by putting in
`n=1,n=2,n=3...` values, you will see:

• Put 1 in
  `n`,
  `71-2.3(1)=68.7`
• Put 2 in
  `n`,
  `71-2.3(2)=66.4`
• Put 3 in
  `n`,
  `71-2.3(3)=64.1`

68.7, 66.4, 64.1, ....

To find common difference (d) (difference in a term and its previous term) we take any term and subtract from it the term before it:

`66.4-68.7=-2.3`

The sum of arithmetic series formula is:

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

Where,

• 
  `S_(n)` is the sum of nth term
• a is the first term (in our case it is 68.7)
• n is the term number (in our case we want to find 50th sum, so n = 50)
• d is the common difference (in our case it is -2.3)

Substituting these values, we get:

`S_(50)=(50)/(2)[2(68.7)+(50-1)(-2.3)]\\S_(50)=25[137.4+(49)(-2.3)]\\S_(50)=25[24.7]\\S_(50)=617.5`

Last answer choice is right.