Evaluate: \bf{\sum^(32)_(n=1)\:(2n+8) Please help A.S.A.P., thank you guys! Please show work as well. \bigstar

Question

Evaluate:


`\bf{\sum^(32)_(n=1)\:(2n+8)`

Please help A.S.A.P., thank you guys!

Please show work as well.


`\bigstar`

Answer 1

S₃₂ = 1312

Step-by-step explanation:

`\boxed{\sf \sum _(n=1)^(32)\left(2n+8\right)}`

Formula Required:

`\sf sum \ of \ arithmetic \ series = (n)/(2) (2a \ + \ (n-1) \ d)`

Identify the following's:

• First Term (a) = (2(1) + 8) = 10

• Common Difference (d) = 2nd term - first term = (2(2) + 8) - (2(1) + 8) = 2

• Total Terms (n) = 32

Insert variables:

`\rightarrow \ \sf S_(32) = (32)/(2) (2(10) + (32-1) 2) \quad \xrightarrow{\text{Simplify} } \quad 1312`