The values of the first and last terms are given. How many terms are there in the arithmetic sequence?
8, 4, 0, - 4
Practice makes perfect
We want to find the arithmetic means in the given arithmetic sequence. To do so, we first have to find the value of the common difference d.
12, ?, ?, ?,?, - 8
We see that the first term is a_1= 12, and there are 6 total terms. Therefore, we have that n= 6. We can substitute these two values in the general formula for the n^(th) term of an arithmetic sequence.
a_n= a_1+( n-1)d ⇓ a_6= 12+( 6-1)d
We are also given the value of the last term, - 8. Since n=6, we have that a_6=- 8. We can substitute this in the above formula and solve for d.
