Question

In the first week of the Year, Nancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks? $1,326

Answer 1

Nacy would save 1,378 dollar if she perofrm this saving plan.

Step-by-step explanation:

It will be an Euler sum

`1 + 2 + 3 + 4 + ... + 50  + 51 + 52= Sn\\\\(n * (n+1))/(2)  = Sn`

In this case the last term is 52

`(52 * (52+1))/(2)`

Sn = 1.378‬

The explanation is that we can arrenge the term to generate sum of 53:

1 + 52

2 + 51

3 + 50

.......

25+28

26 + 27

In total there is 26 of this sums

53 x 26 = 1,378

If we notice 26 is half the value of n so we got:

`(52)/(2) * 53`

we can also express 52 in term of n+1 achieving the Sn formula:

`(52)/(2) * (52 + 1)`