Question

Find the sum of the first 100 terms of the arithmetic sequence with the first term 2 and the common difference 5. plz only answer if you actually have read the question and know the answer.

Answer 1

24950

Explanation:

100th term is 497 and we then use the gause method which is (1+497)*497/2

Answer 2

25,200

Explanation:

To find the sum of an arithmetic series, one can use the formula for an arithmetic series: n×
`((term 1)+(final term))/(2)`=the sum of the series.

To find the final term we need to use the rule: the first term is 2, so you will have to add on two at the end, and then each term is 5 larger than the last, so if you want to quickly calculate the 100th term you can multiply (which is basically just fast addition). The formula for the 100th term is 5(100)+2=502.

Now you have all of the necessary parts for the sum of the series formula: n=100, first term=2, final term=502.

100×
`(2+502)/(2)`=100×
`(504)/(2)`=100×252=25,200.