Answer: (assuming the first three terms are -6, -2, 2)
(a) f(n) = 4n - 10
(b) 30
Explanation:
(So, just as a preface, I made this answer assuming the first three terms are -6, -2, and 2 since I couldn't find a provided fourth term as the problem said)
(a) In order to create an equation for an arithmetic sequence, you need to find the common difference(d) and the 0th term. You can find the common difference by finding the difference between two consecutive terms:
2 - (-2) = 4 (or (-2) - (-6) = 4), so d = 4
Now, you need to find the 0th term. To do this, you can just subtract the d from the first term, -6:
-6 - 4 = -10.
At this point, you can write the equation:
f(n) = -10 + 4n (this is the 0th term plus the common difference, 4, times the nth term)
f(n) = 4n - 10 (reorganize by value of exponents)
(b) In order to find the 10th term, you just need to plug it into the previous equation:
where n = 10, and f(n) = 4n - 10,
f(n) = 4(10) - 10 (substitute n into the equation)
f(n) = 40 - 10 (multiply the term in the parenthesis by the constant)
f(n) = 30 (subtract)