Answer:
The answer is 286.
Explanation:
We first find the first term of the sequence, a₁. We use the explicit formula for an arithmetic sequence to do this:
We know the 6th term is 22; this means we substitute 6 in for n. We also know the common difference is 6, so we use that for d. That gives us a₆=a₁+6(6-1).
We know the value of the sixth term is 22, so we use that instead of a₆:
22=a₁+6(6-1).
Evaluating this, we have
22=a₁+6(5)
22=a₁+30.
Subtract 30 from both sides, and we have
22-30=a₁
-8=a₁.
We now use this value in our explicit formula:
To find the fiftieth term we replace n with 50:
a₅₀= -8+6(50-1)
a₅₀= -8+6(49)
a₅₀= -8+294
a₅₀=286
