Question

Please help I cannot figure this out, different ai give me different answers

Answer 1

The sum of the series
`\sum\limits_(j=3)^(40)5+2\cdot j` is 1824

How to find the sum of the series

The sum
`\sum\limits_(j=3)^(40) 5+2\cdot j`is an arithmetic series, where the first term can be obtained by plugging in j = 3 in the equation 5 + 2·j, which is; 5 + 2 × 3 = 11, and the common difference,d, is; (5 + 2 × 4) - (5 + 2 × 3) = 2

The number of terms between 3 and 40, n, are 40 - 3 + 1 = 38 terms

The formula for the sum of an arithmetic series is; Sₙ =
`(n)/(2) \cdot (2\cdot a+(n - 1)\cdot d)`

Therefore; the sum of the arithmetic series is; S₃₈ =
`(38)/(2) * (2* 11+(38 - 1)* 2)`

S₃₈ =
`19 * (22+74)`

S₃₈ = 19 × 96

19 × 96 = 1824

S₃₈ = 1824