The answer can be found by assuming that we have an arithmetic progression that stars in 53 with a common difference of 7. The equation for the sum of an arithmetic progression up to n terms is given by:
[tex]s_n=\frac{n}{2}(2a+(n-1)d)[/tex]Where, for this case
[tex]a=53\text{ , }n=20\text{ and }d=7[/tex]So, applying the equation with these data, we obtain:
[tex]\begin{gathered} s_{20}=\frac{20}{2}(2(53)+(20-1)7) \\ s_{20}=10(106+19(7)) \\ s_{20}=10(106+19(7))=10(239)=2390 \end{gathered}[/tex]Thus, the sum up to 20 terms of the given series is 2390.
