 # Math Book 1: Sequences & Series

Arithmetic Progression and Geometric Progression

Sequences and series including progressions questions may appear in GMAT quant section. You could expect 1 to 2 questions covering this concept in both variants - GMAT Problem Solving (mainly as a word problem) and GMAT Data Sufficiency.

### Concepts Covered

A typical series tested includes arithmetic progression and geometric or multiplicative progression. Wizako's GMAT Math Lesson Book in this chapter covers the following concepts in sequences, series and progressions:

1. Introduction to Arithmetic Progression.
2. Explanation with formulae to find the nth term of an arithmetic progression and the sum of n terms of an arithmetic progression.
3. Illustrative and solved examples to find the value of the common difference, first term and the number of terms, given the sum of n terms or the nth term and first term of an AP.
4. What happens to an AP when a constant is added to or subtracted from each term of the sequence?
5. What happens to an Arithmetic Sequence when a constant is multiplied to each term of the sequence or when each term of the sequence is divided by a constant?
6. Introduction to Multiplicative Progression or Geometric Progression (GP).
7. Formulae to find the nth term of a multiplicative progression and the sum up to n terms of a multiplicative progression.
8. Introduction to the concept of infinitely decreasing geometric progression and the formulae to find the sum of such a sequence.
9. Geometric Mean of a sequence in geometric progression.
10. What happens when each term of a Multiplicative Progression is multiplied by a constant?
11. Relation between Arithmetic mean and Geometric Mean.
12. 2 illustrative examples to explain concepts; 22 solved examples (with shortcuts wherever applicable) to acquaint you with as many different questions as possible; 17 exercise problems with answer key and explanatory answers to provide you with practice and a timed multiple choice test with 37 medium to hard questions. Explanatory answers and answer key are provided for the test.

Here is a typical solved example from this chapter.

### Sample Question

There are 4 terms in an A.P. such that the sum of the two means is 21 and the product of the extremes is 54. What are the terms of the A.P?

A better way to represent 4 terms in AP
Let the four terms be a - 3d, a - d, a + d and a + 3d.

The sum of the two means = sum of the middle two terms
i.e., (a - d) + (a + d) = 2a = 21
or a = 10.5

The product of the two extremes = product of the first and the last term
i.e., (a - 3d)(a + 3d) = 54
a2 - 9d2 = 54
10.52 - 9d2 = 54
9d2 = 110.25 - 54 = 56.25
3d = 7.5
So, d = 2.5.

The four terms of the arithmetic progression are

1. a - 3d = 10.5 - 7.5 = 3
2. a - d = 10.5 - 2.5 = 8
3. a + d = 10.5 + 2.5 = 13 and
4. a + 3d = 10.5 + 7.5 = 18.
##### Note

In the above expression, the term 'a' is not the first term as is generally the case in most AP questions and the common difference is not 'd'. There is actually no term as 'a' as part of this progression. The terms are a - 3d, a - d ... and the common difference is 2d.

### Chapterwise details of Wizako's Math Lesson Books

Math Lesson Book 1

 1 Linear Equations Details 2 Quadratic Equations Details 3 Set Theory Details 4 Sequences & Series Details 5 Number Properties & Theory Details 6 Inequalities Details 7 Functions

Math Lesson Book 2

 1 Descriptive Statistics Details 2 Ratio Proportion Details 3 Mixtures 4 Interest 5 Rates: Speed Distance Details 6 Rates: Races Details 7 Rates: Work Time Details

Math Lesson Book 3

 1 Percents Details 2 Profits Details 3 Permutation Combination Details 4 Probability Details 5 Geometry Details 6 Solid Geometry 7 Coordinate Geometry Details