Question

In a sequence of numbers, a4= 98, a5= 99.2, a6= 100.4, a7= 101.6, and a8= 102.8. Based on this information,which equation can be used to find an, the nth term in the sequence?

Answer 1

Given:

a4 = 98

a5 = 99.2

a6 = 100.4

a7 = 101.6

a8 = 102.8

Use the arithmetic sequence formula below:

$a_n=a_1+(n-1)d$

Where,

an = nth term

a1 = first term

n = number of terms

d = common differnce

Let's solve for the common differnce.

d = a5 - a4 = 99.2 - 98 = 1.2

Use the 8th term a8, to find the first term:

$\begin{gathered} 102.8=a_1+(8-1)1.2_{} \\ \\ 102.8=a_1+(7)1.2 \\ \\ 102.8=a_1+8.4 \\ \\ a_1=102.8-8.4\text{ = 94.4} \end{gathered}$

Therefore, the first term a1 = 94.4

Thus, the equation for the nth term will be:

Input 94.4 for a1, 1.2 for d in the arithmetic formula above

$\begin{gathered} a_n=94.4+(n-1)1.2 \\ \\ a_n=94.4+1.2n-1.2 \\ \\ \text{combine like terms:} \\ a_n=1.2n+94.4-1.2 \\ \\ a_n=1.2n+93.2 \end{gathered}$

ANSWER:

$a_n=1.2n+93.2$