# 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.

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.