Write a recursive formula for the sequence 5, 18, 31, 44, 57, ... Then find the next term. I’m thinking that the answer is A.
A. a1=-8; an=an-1+13. The next term is 70
B. a1=5; an=an-1+13. The next term is 70
C. a1=5; an=an-1-13. The next term is 83
D. a1=-8; an=an-1-13. The next term is 83
Hmmm. close, but what is the first term (a1)?
a with a small 1 next to it a_1
yes, but a1 is 5, not -13 !
To find a recursive formula for the given sequence, let's examine the pattern. Notice that each term in the sequence is obtained by adding 13 to the previous term. We can represent this pattern using a recursive formula.
Let's represent the first term as a1 and the nth term as an. Since the first term is 5, we have a1 = 5. The recursive formula is then an = an-1 + 13, where an-1 represents the previous term.
Now, let's find the next term in the sequence. Substitute n = 6 into the formula:
a6 = a6-1 + 13 = a5 + 13
We know that a5 is the last given term in the sequence, which is 57. So, we can substitute a5 = 57 into the formula:
a6 = 57 + 13 = 70
Therefore, the next term in the sequence is 70.
Now let's look at the answer options:
A. a1 = -8; an = an-1 + 13. The next term is 70.
B. a1 = 5; an = an-1 + 13. The next term is 70.
C. a1 = 5; an = an-1 - 13. The next term is 83.
D. a1 = -8; an = an-1 - 13. The next term is 83.
From our calculations, we determined that the next term in the sequence is 70. Looking at the options, we can see that options A and B both state that the next term is 70. Therefore, either option A or B could be the correct answer.
To choose between options A and B, let's recall the given information: the first term in the sequence is 5. Since option B correctly represents the first term as a1 = 5, we can conclude that option B, "a1 = 5; an = an-1 + 13," is the correct answer.
So, the answer is B.