contestada

Question: Antonio is working with a new geometric series generated by the equation A(n)=20(1.1)^n-1.His sister challenged him to find the sum of the first 22 terms

Question Antonio is working with a new geometric series generated by the equation An2011n1His sister challenged him to find the sum of the first 22 terms class=

Respuesta :

ashish4112119

Answer:

sum of 22nd = 1,428.05

sum of 23 to 40 is 932.53

Step-by-step explanation:

A(n)=20(1.1)^n-1

20 is the first term or a1

1.1 is the common ratio or r

A(22) = 20(1.1)^22-1

22nd term = 20(1.1)^21

22nd term = 148.00

sum of geometric sequence

formula

Sn = a1(1-r^n)/1-r

Sn = sum

a1 = first term

n = number of term

r = constant ratio

sum of 22nd = 1,428.05.

23 to 40 is 17 terms

Sequence: 23, 25.3, 27.83, 30.613, 33.6743, 37.04173, 40.745903 ...

The 17th term: 105.684378686

Sum of the first 17 terms: 932.528165548

socratic

miniwebtoolcomgeometricsequencecalculator

His sister challenged him to find the sum of the first 22 terms of geometric series is 1428.05.

What is a series?

A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.

Antonio is working with a new geometric series generated by the equation that is

[tex]A_{n}=20(1.1)^n-1.[/tex]

His sister challenged him to find the sum of the first 22 terms will be given as

[tex]Sn = \dfrac{a(r^n - 1) }{ (r - 1)}[/tex]

We have

a = 20

r = 1.1

n = 22

Then

[tex]\rm S_n = \dfrac{20(1.1^{22} - 1) }{ (1.1 - 1)}\\\\\\S_n = \dfrac{20(8.14 - 1) }{ 0.1}\\\\\\S_n = \dfrac{20*7.14 }{0.1}\\\\\\S_n = 1428.05[/tex]

His sister challenged him to find the sum of the first 22 terms of geometric series is 1428.05.

More about the series link is given below.

https://brainly.com/question/10813422

Otras preguntas