Question

The pattern starts at 3 and adds 5 to each term. Write the first five terms ofthe sequence.

Answer 1

Solution:

Given that;

The pattern starts at 3 and adds 5 to each term, i.e.

$\begin{gathered} a=3 \\ d=5 \end{gathered}$

Applying the arithmetic progression formula below

$\begin{gathered} t_n=a+(n-1)d \\ a\text{ is the first term} \\ d\text{ is the common difference} \\ n\text{ is number of terms} \\ t_n\text{ is the nth term} \end{gathered}$

Substitute for a and b into the arithmetic progression formula to find the next term

For the second term, n = 2

$\begin{gathered} t_2=3+(2-1)5 \\ t_2=3+5(1)=3+5=8 \\ t_2=8 \end{gathered}$

For the third term, n = 3

$\begin{gathered} t_3=3+(3-1)5=3+5(2)=3+10=13 \\ t_3=13 \end{gathered}$

For the fourth term, n = 4

$\begin{gathered} t_4=3+(4-1)5=3+5(3)=3+15=18 \\ t_4=18 \end{gathered}$

For the fifth term, n = 5

$\begin{gathered} t_5=3+(5-1)5=3+5(4)=3+20=23 \\ t_5=23 \end{gathered}$

Hence, the first five terms of the sequence are

$3,8,13,18,23$