Question

A certain arithmetic sequence has this explicit formula for the nth term:

an = 12 + (n - 1)(5)
The same sequence has this recursive formula:
an = an-1
+
What number belongs in the blank space in the recursive formula?
A. 5
B. 12
о
C. 17
D. 4

Answer 1

A. 5

Explanation:

I assume the definitions are

an = 12 + (n-1)×5

an = an-1 + blank

if this is correct, then we have

a1 = 12

a2 = 12 + 5 = 17 = a1 + 5

a3 = 12 + 2×5 = 22 = a2 + 5

a4 = 12 + 3×5 = 27 = a3 + 5

...

we see, for an we need to add (n-1) times the number 5 to the initial a1 value.

so every new sequence number is larger by 5 than the previous one.

hence the answer.