GMATPrep Sequence and Interest Problem

[mpaudena]

For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (-1)^(k+1) * 1/2^k. If T is the sum of the first 10 terms in the sequence, then T is

A) greater than 2

B) between 1 and 2

C) between 1/2 and 1

D) between 1/4 and 1/2

E) less than 1/4

(in the 1/2^k only the 2 is raised to the power of k not 1/2).

Also:

An investment of d dollars at k percent simple annual interest yields $600 interest over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?

A) 2d/3

B) 3d/4

C) 4d/3

D) 3d/2

E) 8d/3

If you can please try to break down the steps as I may not be able to make the leaps. Thanks in advance.

[sanjana]

Problem 2)

You need to know the formula for Simple Interest to solve this one.
SI = PRT/100
Where,
P-investment amount
R-Interest rate
T-time period of investment

An investment of d dollars at k percent simple annual interest yields $600 interest over a 2 year period.

From this statement,plugging into the formula we get

600=(d*k*2)/100 --------- eqn1

In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?

We have to find the dollar amount that yields 2400 in 3 years,
again plugging we get

2400=(d'*k*3)/100 (question states that interest is the same)

hence,d'=(2400 * 100)/k*3
From eqn 1 substitute for k interms of d and you will get the answer as d'=8d/3.

[mpaudena]

Wow! You must be scoring in the high 700 - 800 Sanjana. Thanks again. Where did you start off when you begin studying? Were you always good in math? Do you know what thought process would help me to see the way you do?