27 Here are the first four terms of an arithmetic sequence.
- 6 -2 2
(a) Find an expression, in terms of n, for the nth term of this sequence.
(b) Find the 10th term of this sequence.
(2 part question; enter answers for (a) and (b) in the answer box below) *
(3 Points)

(assuming the first three terms are -6, -2, 2)

(a) f(n) = 4n - 10

(b) 30

Step-by-step 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)

the answer is 510

step-by-step explanation:

15 • 13 = 195

15 • 12 = 180

15 • 5 = 75

12 • 5 = 60

195 + 180 = 375

375 + 75 = 450

450 + 60 = 510