The values of the first and last terms are given. How many terms are there in the arithmetic sequence?
59/3, 73/3
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.
15, , , 29
We see that the first term is a_1= 15 and there are 4 total terms. Therefore, we have that n= 4. We can substitute these two values in the general formula for the nth term of an arithmetic sequence.
a_n= a_1+( n-1)d ⇓ a_4= 15+( 4-1)d
We are also given the value of the last term, 15. Since n=4, we have that a_4=29. Let's substitute this into our formula and solve for d.
Before we identify the means, let's rewrite the first and the fourth terms of the sequence as fractions.
a_1=15 = 45/3 [0.8em] a_4=29 = 87/3
We can now use the obtained common difference to calculate the two arithmetic means.
