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sum formula

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by bacali » Sat Nov 29, 2008 6:46 am
Q14:

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?

A. $1,326
B. $1,352
C. $1,378
D. $2,652
E. $2,756

Need a lil help

OA: C
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by dmateer25 » Sat Nov 29, 2008 7:07 am
This is an arithmetic progression.

The arithmetic progression formula:

a(n)=a1+(n-1)d

where a1 is the first number
n is a certain number in a sequence
and d is the common difference

a1=1
d=1
n=52

a(n)=1+(52-1)(1)
=52

So Nancy saves 52 during the last week.

Now the formula for finding the sum of consecutive integers is:

n(n+1)/2 where n is the last term

52(52+1)/2

(52*53)/2

1378
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by parallel_chase » Sat Nov 29, 2008 7:49 am
Here is one step process

1st week = $1
2nd week = $2 = 1+1
3rd week = $3 = 2+1...so on

sum of n terms = n/2 [ 2a + (n-1)d]

You can look at the above post for the what each variable stands for

52/2 [ 2*1 + (52-1)*1] = 26 [2+51] = 26*53 = 1378

Hope this helps.
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Re: sum formula

by sudhir3127 » Sat Nov 29, 2008 9:41 am
bacali wrote:Q14:

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?

A. $1,326
B. $1,352
C. $1,378
D. $2,652
E. $2,756

Need a lil help



OA: C
Agree with Chase.. Its in Arithemtic progression
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by cramya » Sat Nov 29, 2008 11:33 am
Another formula for Sn(SUM OF N TERMS) of an AP (aritmetic progression is)

Sn = n(a1+an)/2

where n->number of terms in the sequence
a1-> first term
an->last term

Sn = 52(1+52)/2 = 26*53 = 1378

C)
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by cabando » Sun Dec 30, 2012 4:33 am
we must learn the formula for finding the sum of consecutive integers don't we? I tried to do it but just arrived to know that on week 52 she had earned $52, from there, I didn't know how to work through the problem.
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by Brent@GMATPrepNow » Sun Dec 30, 2012 8:34 am
bacali wrote: 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?

A. $1,326
B. $1,352
C. $1,378
D. $2,652
E. $2,756
Here's another approach (that doesn't require formulas).

We want to add 1+2+3+4+...+51+52
So, let's add them in pairs, starting from the outside and working in.
1+2+3+4+...+51+52 = (1+52) + (2+51) + (3+50) + . . .
= 53 + 53 + 53 + ....

How many 53's are there in our new sum?
Well, there are 52 numbers in the sum 1+2+3+..+52, so there must be 26 pairs, which means there are 26 values in our new sum of 53 + 53 + 53 + ....

So, what is (26)(53)?
Fortunately, if we examine the answer choices, we see that we don't even need to calculate (26)(53)

Why not?
Notice that when we multiply (26)(53), the units digit in the product will be 8 (since 6 times 3 equals 18).

Since only 1 answer choice (C) ends in 8, the correct answer must be C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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