The sum of the first n terms in a geometric sequence given the first term (a1) and the common ratio (r) is calculated through the equation,
<span>Sn </span>= (<span><span><span>a1</span>(1−<span>r^n</span>) / (</span><span>1−r)
Substituting the known terms,
Sn = (20)(1 - (1/4)^4)) / (1 - 1/4)
Sn = 26.5625
Thus, the sum of the first four terms is 26.5625. </span></span>
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Answer:
The formula for compound interest is P (1 + r/n)^(nt), where P is the initial principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods.
Answer:
A. The coefficients of the sum are whole numbers and the sum is a polynomial.
Step-by-step explanation:
The approach to demonstrate the closure property for the sum consists in defining what a polynomial is and demonstrate that the sum of two polynomials with integer coefficients is equal to a polynomial with integer coefficients. We proceed to show the proof below:
1) 
, 
Given
2) 
Definition of addition
3) ![(5\cdot m +2\cdot m ) +[(-3)+4]](https://tex.z-dn.net/?f=%285%5Ccdot%20m%20%2B2%5Ccdot%20m%20%29%20%2B%5B%28-3%29%2B4%5D)
Definition of substraction/Associative and Commutative properties
4) 
Distributive property/Definition of substraction
5) 
Definition of addition/Result
Hence, the coefficients of the sum are whole numbers and the sum is a polynomial. The correct answer is A.
