Question

Write an explicit and a recursive formula for the sequence.

6, 13, 20, 27, 34,
Write an explicit formula.
an ="

a) 7n - 1

b) 6n + 3

c) 8n - 2

d) 9n - 3

Answer 1

The explicit formula for the sequence 6, 13, 20, 27, 34 is an = 7n - 1. The recursive formula is a1 = 6 and an = a(n-1) + 7 for n > 1.

Step-by-step explanation:

To find the explicit formula for a sequence, we look at the pattern of the numbers provided: 6, 13, 20, 27, 34. We can see that each term increases by 7 from the previous one. To get from the first term which is 6 to any term in the sequence, we can multiply the position number (n) by 7 and then subtract 1 to adjust since the first term does not fit the pattern of multiplying by 7 directly. Therefore, the explicit formula would be an = 7n - 1.

The recursive formula for the sequence requires a starting value and a rule to get from one term to the next. The first term is given as 6, and since each term increases by 7, the recursive formula is a1 = 6 and an = a(n-1) + 7 for n > 1.