An arithmetic sequence has t1 = 3, t2 = 10. find tn, sn.

see explanation

Step-by-step explanation:

the n th term of an arithmetic sequence is

= + (n - 1)d

given = 3 and = 10, then

= 3 + d = 10 ⇒ d = 10 - 3 = 7

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

the sum to n terms of an arithmetic sequence is

= [2 + (n - 1)d ]

                        = [(2 × 3) + 7(n - 1) ]

                        = (6 + 7n - 7 )

                        = (7n - 1)

                        = n² - n

she will travel a distance in the range of 3 - 11 miles