A certain arithmetic sequence has this explicit formula for the nth term:an = 13 + (n – 1)(6)The same sequence has this recursive formula:an = an–1 + ________What number belongs in the blank space in the recursive formula?A.19B.5C.13D.6SUBMITarrow_backPREVIOUS
Question
A certain arithmetic sequence has this explicit formula for the nth term:an = 13 + (n – 1)(6)The same sequence has this recursive formula:an = an–1 + ________What number belongs in the blank space in the recursive formula?A.19B.5C.13D.6SUBMITarrow_backPREVIOUS
Solution
The number that belongs in the blank space in the recursive formula is D. 6.
Here's why:
The explicit formula for the nth term of an arithmetic sequence is given by an = a1 + (n – 1)d, where a1 is the first term and d is the common difference.
In the given explicit formula, an = 13 + (n – 1)(6), we can see that the first term a1 is 13 and the common difference d is 6.
In a recursive formula for an arithmetic sequence, the nth term an is found by adding the common difference to the previous term an–1.
So, the recursive formula for the given sequence is an = an–1 + 6.
Therefore, the number that belongs in the blank space in the recursive formula is 6.
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