Write an explicit formula for the recursive formula A(n) = A(n - 1) + 3; A(1) = 6
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Answer:
Step-by-step explanation:
<h3>1. Express as an Equivalent Trinomial</h3>To multiply two binomials (expressions with 2 terms), we can use the FOIL (first, outside, inside, last) method.
We are given this expression:
The expression (x+4) is being squared, which is equal to multiplying the term by itself twice.
Next, multiply the first terms from both binomials, then repeat for the outside, inside, and last terms.
- First: x*x= x²
- Outside: x*4= 4x
- Inside: 4 *x= 4x
- Last: 4*4= 16
Put the products into one expression.
Combine like terms. 4x and 4x both have the variable x, so they can be combined.
Next, substitute 1 in for x in both the original expression and the trinomial we found. If they are equivalent, the results will be the same.
1. (x+4)²
(1+4)²
(5)² = <u>25</u>
2. x²+8x+16
(1)²+8(1)+16
1+8(1)+16
1+8+16
9+16= <u>25 </u><u />
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If x=1, both the original binomial and trinomial equal 25, so we know they are equivalent.