Question

PLEASE HELP ASAP

I think it’s supposed to be an arithmetic series or sequence.

Kaydence is saving for an RRSP. She saved $100 the first year, $200 the second year, $300 the third year, and so on. If she put $100 away on January 1, 2014, $200 away on January 1, 2015, and continued to put money away on the first of each year, how much money would Kaydence have saved by the end of the day on January 1, 2050?

Answer 1

$70,300

Explanation:

The amount Kaydence saved is the value of an arithmetic series with first term 100 and common difference 100. The number of terms in the sum is 37. The formula for the sum can be used.

Sum of an arithmetic series

The formula for the sum of n terms of an arithmetic series is ...

Sn = (2a1 +d(n -1))(n/2) . . . . . . first term a1, common difference d

Application

The number of terms being added is ...

2050 -2014 +1 = 37 . . . . . . years Kaydence made deposits

The formula with a1=100, d=100, and n=37 is ...

`S_(37)=(2\cdot100+100(37-1))(37)/(2)=((200+3600)\cdot37)/(2)\\\\S_(37)=70,\!300`

Kaydence would have saved $70,300 by the end of Jan 1, 2050.