Question

A radio station advertises a contest with ten cash prizes totaling $5510. There is to be a $100 difference between each successive prize.

Find the amounts of the least and greatest prizes the radio station will award.

a.
least: $100
greatest: $1000
b.
least: $10
greatest: $5500
c.
least: $101
greatest: $1001
d.
least: $50
greatest: $1500



Please select the best answer from the choices provided


a) A
b) B
c) C
d) D

Answer 1

option C

c. least: $101

greatest: $1001

Explanation:

A radio station advertises a contest with ten cash prizes totaling $5510. There is to be a $100 difference between each successive prize.

Sum of 10 prizes = 5510

100 is the difference. there is a common difference d=100

So its a arithmetic sequence

the sum formula for arithmetic sequence is

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

Sn = 5510, n=10 n d= 100 we need to find out first term a1

`5510 = (10)/(2)(2a_1 +(10-1)100)`

5510 = 5 (2a1 + 900)

5510 = 10a1 + 4500

Subtract 4500 on both sides

1010= 10a1

divide by 10 on both sides

a1 = 101

so first term that is least term is 101

To find out greatest term we use formula

`a_n = a_1 + (n-1) d`

a(10) = 101 + (10-1)100

= 101 + 900= 1001

greatest is 1001