Find the first five terms in sequences with the following nth terms.

a. {eq}2n^2 + 6 {/eq}

b. {eq}5n + 2 {/eq}

c. {eq}10^n - 4 {/eq}

d. {eq}2n -1 {/eq}

## Question:

Find the first five terms in sequences with the following nth terms.

a. {eq}2n^2 + 6 {/eq}

b. {eq}5n + 2 {/eq}

c. {eq}10^n - 4 {/eq}

d. {eq}2n -1 {/eq}

## Sequence and Series:

A sequence of numbers are defined such that there is the same relationship between each consecutive term, and each of the terms can be once we find the function that describes the nth term of the sequence.

## Answer and Explanation: 1

a. {eq}a_n=2n^2+6 {/eq}

Each of the terms can be found by inputting n=0,1,2...4 in the term above.

{eq}a_0=2(0)^2+6=6 {/eq}

{eq}a_1=2(1)^2+6=8 {/eq}

{eq}a_2=2(2)^2+6=14 {/eq}

{eq}a_3=2(3)^2+6=33 {/eq}

{eq}a_4=2(4)^2+6=38 {/eq}

Hence, the first five terms are** 6, 8, 14, 33, 38.
**

b. {eq}a_n=5n+2 {/eq}

{eq}a_0=5 \times 0+2 = 2 {/eq}

{eq}a_1=5 \times 1+2 = 7 {/eq}

{eq}a_2=5 \times 2+2 = 12 {/eq}

{eq}a_3=5 \times 3+2 = 17 {/eq}

{eq}a_4=5 \times 4+2 = 22 {/eq}

The first five terms are **2, 7, 12, 17, 22. **

c. {eq}a_n=10^n-4 {/eq}

{eq}a_0=10^0-4=1-4=-3 {/eq}

{eq}a_1=10^1-4=10-4=6 {/eq}

{eq}a_2=10^2-4=100-4=96 {/eq}

{eq}a_3=10^3-4=1000-4=996 {/eq}

{eq}a_4=10^4-4=10000-4=9996 {/eq}

The first five terms are **-3, 6, 96, 996, 9996.
**

d. {eq}a_n=2n-1 {/eq}

{eq}a_0=2 \times 0-1=-1 {/eq}

{eq}a_1=2 \times 1-1=1 {/eq}

{eq}a_2=2 \times 2-1=3 {/eq}

{eq}a_3=2 \times 3-1=5 {/eq}

{eq}a_4=2 \times 4-1=7 {/eq}

The first five terms are **-1,1,3,5,7.
**

#### Learn more about this topic:

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Chapter 12 / Lesson 1Learn about the definition of sequence in math. Understand what finite and infinite mathematical sequences are and how they are represented. See examples of famous mathematical sequences that are commonly used.