- Use an appropriate formula to calculate how many terms there are in the sequence 2, 10, 50, ...31250.

*please put full solution

7 terms

Step-by-step explanation:

There is a common ratio between consecutive terms, that is

r = 10 ÷ 2 = 50 ÷ 10 = 5

This indicates the sequence is geometric with nth term

= a₁

where a₁ is the first term and r the common ratio

Here a₁ = 2 and r = 5, then equating to 31250 and solving for n

2 × = 31250 ( divide both sides by 2 )

= 15625 =

Since bases on both sides are equal, both 5, equate exponents

n - 1 = 6 ( add 1 to both sides )

n = 7

That is there are 7 terms in the sequence

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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