What is the formula for a arithmetic series and how can you use it in a practical situation? show explanation!

A finite geometric series is that where the consecutive terms have a fix ratio.

Call r the ratio, An the nth term and An+1 the next term to n, then:

An+1 / An = r

For example, the geometric series, 1, 3, 9, 27, 81, ..

You can verify that

3 = 1* 3

9 = 3 * 3

27 = 9 * 3

81 = 27 * 3

So, the formula is An+1 = An * r, so if you know the first term you can find any other term.

For example, Find the fifth term of a geometric series where the first term is 5 and the second term is 25.

r = second term / first term = 25 / 5 = 5

=> Fifth term = First term * r * r * r * r = First term * r^4 = 25 * 5^4 = 15,625

From this you can also see this valid formula:

An = A1 * r^ (n-1).

So now you have two equivalent formulas:

An+1 = An * r, which is called recursive formula, and

An = A1 * r ^ (n-1), which is called explicit formula

hope this helps :)

ddd

step-by-step explanation:

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!