Question

Find the 10th term of the sequence defined by the given rule. Assume that the domain of each function is the set of whole numbers greater than 0.

f(1) = 20, f(n) = 3 x f(n-1) - 70
a) -5
b) -10
c) 5
d) 10

Answer 1

To find the 10th term of the given sequence, use the recursive formula f(n) = 3 x f(n-1) - 70, starting with f(1) = 20. Calculate each term using the formula, and continue the pattern until you reach the 10th term.

Step-by-step explanation:

The given sequence is defined by the rule: f(1) = 20 and f(n) = 3 x f(n-1) - 70.

To find the 10th term, we can use the recursive formula. Start with the first term, f(1) = 20. Then use the formula: f(2) = 3 x f(1) - 70 = 3 x 20 - 70 = -10. Now we can continue this pattern for the next terms:

1. f(3) = 3 x f(2) - 70 = 3 x (-10) - 70 = -100
2. f(4) = 3 x f(3) - 70 = 3 x (-100) - 70 = -370
3. f(5) = 3 x f(4) - 70 = 3 x (-370) - 70 = -1180
4. And so on.

Using this pattern, we can calculate the 10th term:

f(10) = 3 x f(9) - 70 = 3 x (-2,770) - 70 = -8,380.