Question

Calculate s50 for the arithmetic sequence defined by

Answer 1

Answer:

617.5

Step-by-step 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:

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

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:

$S_{50}=\frac{50}{2}[2(68.7)+(50-1)(-2.3)]\\S_{50}=25[137.4+(49)(-2.3)]\\S_{50}=25[24.7]\\S_{50}=617.5$

Last answer choice is right.

Answer 2

Answer: D. 617.5 hope that helps !