Question

The amount of money in Nadia’s savings account is represented by the recursive formula an=1.025(an-1)+50 if a6=291.51 what are the first two numbers in the sequence?
A. $25.36, $75.99
B. $50.00, $101.25
C. $101.25, $153.78
D. $75.99, $127.89

Answer 1

Recursive formula is one way of solving an arithmetic sequence. It contains the initial term of a sequence and the implementing rule that serve as a pattern in finding the next terms. In the problem given, the 6th term is provided, therefore we can solve for the initial term in reverse. To make use of it, instead of multiplying 1.025, we should divide it after deducting 50 (which supposedly is added).

Therefore, we perform the given formula: A (n) = 1.025(an-1) + 50
a(5) =1.025 (235.62) + 50 = 291.51

a(4) = 1.025 (181.09) + 50 = 235.62

a(3) = 1.025 (127.89) + 50 = 181.09

a(2) = 1.025 (75.99) + 50 = 127.89

a(1) = 1.025 (25.36) + 50 = 75.99

a(n) = 25.36

The terms before a(6) are indicated above, since a(6) is already given.

So, the correct answer is A. $25.36, $75.99.