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{ = }(2)/(3)\cdot1+(5)/(6)=(2)/(3)+(5)/(6)=(3)/(2)`
`a36=(2)/(3)\cdot36+(5)/(6)=(72)/(3)+(5)/(6)=(149)/(6)`
`S_(36)=(36)/(2)((3)/(2)+(149)/(6))`

That is the full solution.