Number of terms:
1. Find the common difference: Subtract the first term from the second:
[tex]6-2=4[/tex]
2. Us the last term (tn), first term (a1), and common difference (d) in the next equation to solve (number of terms (n):
[tex]t_n=a_1+(n-1)d[/tex]
[tex]\begin{gathered} 98=2+(n-1)4 \\ \text{Subtract 2 in both sides of the equation:} \\ 98-2=2-2+(n-1)4 \\ 96=(n-1)4 \\ \\ \text{Divide both sides of the equation into 4:} \\ \frac{96}{4}=\frac{(n-1)4}{4} \\ \\ 24=n-1 \\ \\ Add\text{ 1 in both sides of the equation:} \\ 24+1=n-1+1 \\ 25=n \\ \\ \\ n=25 \end{gathered}[/tex]Number of terms: 25
Sum of the terms:
[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex][tex]\begin{gathered} S_{\mleft\{25\mright\}}=\frac{25(2+98)}{2} \\ \\ S_{\mleft\{25\mright\}}=\frac{25(100)}{2} \\ \\ S_{\{25\}}=\frac{2500}{2} \\ \\ S_{\{25\}}=1250 \end{gathered}[/tex]Sum of the series: 1250
