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}

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.