GMAT Math: Progressions

Written by Kelly Granson. Posted in GMAT Study Guide

Math equation_dice_d6Introduction

Sequence and series is one of the most interesting topics for GMAT test takers. A progression consists of a series of numbers in a given order. A constant relation exists between every pair of consecutive terms of a sequence. In general, there are three types of progressions.

1) Arithmetic progression

2) Geometric progression

3) Harmonic progression

In the GMAT, arithmetic and geometric progressions will play a key role. So let us discuss them in detail.

Arithmetic Progression

Arithmetic progression is a sequence of numbers in which the difference between any pair of consecutive numbers is same.

• Example: 4,7,10,13,16,19,22,25,28...

The difference between any two consecutive terms in the above sequence is 3, making this an arithmetic progression.

Property of arithmetic sequence

07.02

Nth term of arithmetic progression

07.021

07.022

07.023 is the nth term.

07.024 is the first term.

07.025 is the nth term.

07.026 is the common difference between any two consecutive terms.

Example:

Find the nth term of the following sequence: 3, 8, 13, 18, 23, 28, 33, 38...

Find the 100th term of this sequence.

07.027

07.028

07.029

07.030

07.031

07.032

The 100th term of the sequence is 503.

Sum of n terms of arithmetic progression

07.033 07.034 is the last term and 07.035 is the first term

Or

07.036

Geometric Progression

A geometric progression is a sequence in which every pair of consecutive terms will produce a common ratio. In other words, every term is obtained by multiplying the previous term by a constant number.

07.037

Here, r is the common ratio.

07.038 are the first, second, third, and nth terms respectively.

Geometric progression sequence

This is how a geometric progression looks with respect to the first term.

07.039

Nth term of the geometric progression

07.040

Example:

Given the geometric sequence 3, 6, 12, 24, 48...

Find the 10th term of the sequence.

Here the common ratio is 6/3 = 2.

The 10th term will be:

07.041

07.042

07.043

07.044

Sum of n terms of a geometric progression

The sum of n terms of a geometric progression is given by

07.045

Sum to infinite geometric progression

Geometric progression has the special feature of allowing you to find the sum to infinity. If the number of terms is infinite, then the sum of the terms looks like this:

07.046

PROBLEM:

Find the number of terms in the geometric progression 7, 14, 28, 56...7168

The last term is 7868 . Finding which this term is will tell you the total number of terms in the sequence.

The nth term is given by

07.047

The common ratio is 14/7 = 2.

So r = 2

07.048

07.049

Divide by 7 on both sides:

07.050

07.051

07.052

Multiply by 2 on both sides:

07.053

07.054

2048 is 07.055

So 07.056

As bases are equal, we can equate the exponents. Hence n = 11.

So the number of terms in the sequence is 11. The following sample problem shows that these can be both easy and interesting to solve.

GMAT PROBLEM:

Given a set X that contains the following elements: {y, 0, 3, 6, 9, 12, 15}. What is the value of y if the set contains only whole numbers?

1) -3

2) 18

3) 3

4) Either -3 or 18

5) Doesn't exist

Solution:

Let us remove 'y' and look at the sequence. The difference between each term is 3. Hence we can say that this is an arithmetic progression. So as y is the term just before 0 and we may say that 'y' will be 3 less than that, so we can choose y as -3. But it is given that the set contains only whole numbers. So -3 cannot be the possible option. Nowhere in the question is it mentioned that the terms are in order . We can also say that the term can also be after 15. Hence we can say y is 3 greater than 15. That is 18.

So the answer is 18. Option (B)

Your friends will also love this article. Share!

Related Articles:

Comments: