Question

Which equation could be used to calculate the 36th parial sum for the arithmetic sequence (an)=(2/3n+5/6)

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

an = (2/3n+5/6)

Step 02:

arithmetic sequence (partial sum):

Sn = n/2 (a1 + an)

$a1\text{ = }\frac{2}{3}\cdot1+\frac{5}{6}=\frac{2}{3}+\frac{5}{6}=\frac{3}{2}$$a36=\frac{2}{3}\cdot36+\frac{5}{6}=\frac{72}{3}+\frac{5}{6}=\frac{149}{6}$$S_{36}=\frac{36}{2}(\frac{3}{2}+\frac{149}{6})$

That is the full solution.