Solve for: S_20 and the 5th element of the arithmetic sequence where a_5 = 30 and d=2Show step by step process to explain the solution and answer

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For an arithmetic sequence,

`a_n = a_1+(n-1)d`

and `S_n = n/2(2a_1+(n-1)d)`

The fifth element is 30. Then,

`a_5 = 30 = a_1+(5-1)2`

`a_1 = 22`

The forst element is 22.

Therefore,

`S_20 = 20/2(2(22)+(20-1)2)`

S_20 = 820.

 

The sum of first 20 terms is 820.

Sources:

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