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Greer created a sequence that begins with the number 5. Each term after the first is 4.1 times the amount of the preceding term. Which formula should Greer use to find the sum of the first 23 terms of her sequence?
A.) 23(90.2+5) / 2
B.) 4.1(90.2+5) / 2
C.) 5(1-4.1^23) / 1-4.1
D.) 4.1(1-5^23) / 1-5

Respuesta :

I believe the answer is B.

4.1(90.2+5)/2

we are given

first term is 5

[tex] a_1=5 [/tex]

Each term after the first is 4.1 times the amount of the preceding term

so, this is geometric sequence

now, we can find common ratio

[tex] r=4.1 [/tex]

total number of terms is 23

so,

[tex] n=23 [/tex]

now, we can use geometric sum formula

[tex] Sum=a_1\frac{r^n-1}{r-1} [/tex]

now, we can plug values

and we get

[tex] Sum=5\frac{4.1^{23}-1}{4.1-1} [/tex]

we can also write it as

[tex] Sum=5\frac{1-4.1^{23}}{1-4.1} [/tex]

so, option-C.........Answer

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