Question

Find the arithmetic series, find S25 !!! Show work please

Answer 1

21)

`a_(n)` = a₁ + d(n - 1) ; where a₁ is the first term and d is the difference.

a₁ = 3, d = 4 →
`a_(n)` = 3 + 4(n - 1) = 3 + 4n - 4 = 4n - 1

`a_(25)` = 4(25) - 1 = 100 - 1 = 99

`S_(n)` =
`(a_(1) +a_(n) )/(2)(n)`

`S_(25)` =
`(3 +99 )/(2)(25)` =
`(102 )/(2)  (25)` = 51 · 25 = 1275

Answer:
`a_(n)` = 4n - 1 , 1275

23)

`a_(n)` = a₁ + d(n - 1) ; where a₁ is the first term and d is the difference.

a₁ = 4, d = 10 →
`a_(n)` = 4 + 10(n - 1) = 4 + 10n - 10 = 10n - 6

`a_(25)` = 10(25) - 6 = 250 - 6 = 244

`S_(n)` =
`(a_(1) +a_(n) )/(2) (n)`

`S_(25)` =
`(4 +244 )/(2) (25)` =
`(248)/(2)(25)` = 124 · 25 = 3100

Answer:
`a_(n)` = 10n - 6 , 3100