Question

You invested money in a fund and each month you receive a payment for your investment. Over the first four months, you received $ 50, $ 52, $ 55 , and $ 59 . If this pattern continues, how much will you receive in the tenth month?c. Explain the difference between an explicit formula and a recursive formula. Use your formula from part (a) as part of your explanation.

Answer 1

Money received in tenth month: $104

Difference between explicit formula and a recursive formula is: the use of (n-1)th term, nth term and the common difference (d) brings a great difference between the two formulae of an arithmetic progression.

What is arithmetic progression?

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

• Money received in first four months: $50, $52, $55, %59.

To find: Money received in tenth month.

Finding:

As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.

That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.

Thus, for the tenth month, we can use the formula of recursion, given by: $a_n=a_{n-1}+n$, n ≥ 1.

For a₁ = 50, a₂ = a₁ + 2

=> a₂ = 50 + 2

This way, a₅ = a₄ + 5

=> a₅ = 59 + 5 = 64

a₆ = a₅ + 6

=> a₆ = 64 + 6 = 70

a₇ = a₆ + 7

=> a₇ = 70 + 7 = 77

a₈ = a₇ + 8

=> a₈ = 77 + 8 = 85

a₉ = a₈ + 9

=> a₉ = 85 + 9 = 94

a₁₀ = a₉ + 10

=> a₁₀ = 94 + 10 = 104

Thus, the payment received in tenth month will be $104.

(b) Difference between explicit formula and recursive formula of an arithmetic progression:

• The first term of a recursive formula is a₁ and the formula for the nth term uses the first term and the common difference, d. One example of a recursive formula is $a_n=a_{n-1}+d$.

• A formula for the nth term in an explicit formula would include the initial term a₁, the common difference d, and the term number, n. The equation $a_n = a_1 + (n-1)d$.

To learn more about arithmetic Progressions, refer to the link: brainly.com/question/6561461

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