Answer:
an = 17n - 46
a50 = 804
Explanation:
-29, -12, 5, 22, ...
Subtract each number from the next one.
-12 - (-29) = 17
5 - (-12) = 17
22 - 5 = 17
The common difference is 17. This is an arithmetic sequence which starts with -29, and in which each subsequent value is 17 more than the previous value.
a1 = -29
a2 = -29 + 17
a3 = -29 + 2(17)
a4 = -29 + 3(17)
Notice that for each term, you have -29 and something added to it. What you add to -29 is 17 multiplied by 1 less than the number of the term. For term 1, 1 less than 1 is 0. You add 0 * 17 to -29 and get -29. term 1 is -29. For term 2, 1 less than 2 is 1. You add 1 * 17 to -29 and get -12, etc.
For term n, 1 less than n is n - 1. Add (n - 1) * 17 to -29 to get term n.
an = -29 + 17(n - 1)
This formula can be simplified.
an = -29 + 17n - 17
an = -46 + 17n
an = 17n - 46
a50 = 17(50) - 46
a50 = 804