SEQUENCE AND SERIES PROBLEM SOLUTION

In mathematics, a **sequence** is a list of objects (or events) that have been ordered in a sequential fashion; such that each member either comes before or after, every other member. … A **series** is a sum of a **sequence** of terms. That is, a **series** is a list of numbers with addition operations between them.

**What is the difference between**a

**sequence**and a

**series**? The list of numbers written

**in a**definite order is called a

**sequence**. The sum of terms of an infinite

**sequence**is called an infinite

**series**. … Therefore

**sequence**is an ordered list of numbers and

**series**is the sum of a list of numbers.

**Note:**That there must be a definite rule. A rule that works in a given sequence may not work in another.

The nth term of sequence is given by 1/4(n + 1) (2n – 1) find the first four terms

SOLUTION

**first term**

1/4 (1 + 1) (2 x 1 – 1)

1/4 (1 + 1) (2 – 1)

1/4 (2) (1)

1/4 x 2 =1/2

**second term**

1/4 (2 + 1) (2 x 2 – 1)

1/4 (2 + 1) (4 – 2)

1/4 (3) (3)

1/4 x 9 = 9/4

**third term**

1/4 (3 + 1) (2 x 3 – 1)

1/4 (3 + 1) (6 – 1)

1/4 (4) (5)

1/4 x 20 = 5

**fouth term**

1/4 (4 + 1) (2 x 8 – 1)

1/4 (4 + 1) (8 – 1)

1/4 (5) (7)

1/4 (35) = 35/4

**Therefore** 1/2, 9/4, 5, 35/4 are the the first 4 terms

2. A sequence is given by Tn =n(n – 1). if Tn = 72, find the value of n

SOLUTION

Tn = n(n – 1)= -72

definitely turn that question into an equation been quadratic equation i.e

n^2 – n + 72 = 0

then use the Quadratic formula method or general formula method

your answer will be after using formula method as x = 8 or x = -9

**SOLVE: find the sum of the first 6 terms of 2n – 1** and drop your answer below the comment box

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