Question

The following recursive formula represents the number of prizes offered in each round of a game show.

an = 2, if n = 1
an-1 + 7, if n > 1
Write the explicit formula for the number of prizes and use it to calculate the number of prizes in round 7.

Answer 1

The explicit formula for the number of prizes is an = 7(n-1) + 2. Using this formula, the number of prizes in round 7 is 44.

Step-by-step explanation:

The explicit formula for the number of prizes can be found by substituting the values of n into the recursive formula and simplifying the expression. For n > 1, the formula is: an = 7(n-1) + 2. This formula calculates the number of prizes in round n based on the number of prizes in the previous round.

To find the number of prizes in round 7, we can substitute n = 7 into the explicit formula:

a7 = 7(7-1) + 2

a7 = 7(6) + 2

a7 = 42 + 2

a7 = 44