arithmetic sequences

Question

Find the explicit formula for the nth term of the arithmetic sequence whose initial term and common difference are given. Then, find the specified term.

a₁=-2; d= 4

an= ?

a7= ?

Answer 1

an = a1 + (n - 1)d

an = -2 + (n - 1)4

an = -2 +4n -4

an = 4n - 6

a7 = 4x7 - 6

a7 = 28 - 6

a7 = 22

Now let's do this the 'long' way as a check. (This would obviously not be practical if we were finding a50 not to mention something like aone billion!)

Start with -2 and keep adding 4 until we have 7 terms.

-2, 2, 6, 10, 14, 18, 22 check