Question

determine the number of terms in the arithmetic sequence below

Answer 1

First Term = a = -70

Last Term = 60

$\begin{gathered} \text{The general term for an arithmetic progression goes thus:} \\ T_n=a+(n-1)d \\ \text{where T}_n=An\text{ arbitrary term} \\ n=\text{ ordinal} \\ d=\text{common difference} \\ a=\text{first term} \end{gathered}$

To get n, we substitute the values of the other variables to get n.

$\begin{gathered} \text{Subtract a from both sides} \\ (n-1)d=T_n-a \\ \text{Divide d from both sides} \\ n-1=\frac{T_n-a}{d} \\ \text{Add 1 to both sides} \\ n=\frac{T_n-a}{d}+1 \end{gathered}$

where Tn = last term = 60

a = -70

d = 1

$\begin{gathered} n=\frac{60-(-70)}{1}+1 \\ n=\frac{130}{1}+1=130 \end{gathered}$

n = last ordinal = 130