Question

An arithmetic sequence has t1 = 3, t2 = 10. Find tn, Sn.

Answer 1

see explanation

Explanation:

the n th term of an arithmetic sequence is

`t_(n)` =
`t_(1)` + (n - 1)d

given
`t_(1)` = 3 and
`t_(2)` = 10, then

`t_(2)` = 3 + d = 10 ⇒ d = 10 - 3 = 7

`t_(n)` = 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4

the sum to n terms of an arithmetic sequence is

`S_(n)` =
`(n)/(2)`[2
`t_(1)` + (n - 1)d ]

=
`(n)/(2)`[(2 × 3) + 7(n - 1) ]

=
`(n)/(2)`(6 + 7n - 7 )

=
`(n)/(2)`(7n - 1)

=
`(7)/(2)` n² -
`(1)/(2)` n