Answer:
Step-by-step explanation:
The standard form of an arithmetic sequence is
aₙ = a₁ + d(n - 1)
where aₙ is the number of the term in the sequence (in order from first term where n = 1, to second term where n = 2, to third term where n = 3, etc) a₁ is the the first term in the sequence, and d is the arithmetic difference or means. This is what we are looking to solve for.
In our sequence we have the first term, -3 (where n = 1) and the fifth term, 93 (where n = 5). If we fill in what we have, the only unknown is d, our arithmetic difference (means) between each number in the sequence.
Because we have the fifth term, we can write our standard form to fit our needs:
a₅ = a₁ + d(n-1). Therefore,
93 = -3 + d(5 - 1) and
93 = -3 + d(4) so
96 = 4d and
d = 24
Our arithmetic difference (means) is 24. Let's test it on a few values of n. Let's look for the second, third, and 4th terms, and then try it out for n = 5 to make sure the 5th term, using our arithmetic sequence with d = 24 works and we do, in fact, find the fifth term to be 93.
Testing n = 2
a₂ = -3 + 24(2 - 1) so
a₂ = -3 + 24(1) and
a₂ = 21. Second term is 21 (Notice that difference between -3 and 21 is 24)
Testing n = 3
a₃ = -3 + 24(3 - 1) so
a₃ = -3 + 24(2) and
a₃ = 48 - 3 and
a₃ = 45 (Notice the difference between 21 and 45 is 24)
Testing n = 4
a₄ = -3 + 24(4 - 1) so
a₄ = -3 + 24(3) and
a₄ = 72 - 3 and
a₄ = 69 (Notice the difference between 45 and 69 is 24)
Testing n = 5 (and it better come out as 93 or we did something wrong!)
a₅ = -3 + 24(5 - 1) and
a₅ = -3 + 24(4) so
a₅ = 96 - 3 so
a₅ = 93 (Phew!) ; )
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