A financial forecasting model predicts monthly sales revenue using a sequence where the in… — GRE General Test

A financial forecasting model predicts monthly sales revenue using a sequence where the initial revenue in month 1 is $R_1 = \$80{}000$ , and the revenue for each subsequent month $n$ (for $n \ge 2$ ) is calculated using the recursive formula $R_n = 0.75 R_{n-1} + 5{}000$ . If each monthly revenue figure $R_n$ is rounded to the nearest hundred dollars before summing, what is the estimated total revenue, in dollars, for the first 4 months combined?

Cevap: 244100 dollars

Cevap

The estimated total revenue for the first 4 months combined is 244,100 dollars.

By evaluating the recursive formula

R_n = 0.75 R_{n-1} + 5{}000

for months 1 through 4, we obtain

R_1 = 80{}000

R_2 = 65{}000

R_3 = 53{}750

, and

R_4 = 45{}312.50

. Rounding each to the nearest hundred yields

80{}000

65{}000

53{}800

, and

45{}300

, respectively. Summing these four rounded figures gives

244{}100

Adım Adım Çözüm

Find the first term

R_1

and its rounded value.

R_1 = 80{}000

, which rounds to

80{}000

Given initial term.

Calculate the second term

R_2

using the recursive formula and round it.

R_2 = 0.75(80{}000) + 5{}000 = 65{}000

, which rounds to

65{}000

Apply

R_2 = 0.75 R_1 + 5{}000

Calculate the third term

R_3

using unrounded

R_2

and round to the nearest hundred.

R_3 = 0.75(65{}000) + 5{}000 = 53{}750

, which rounds to

53{}800

Apply

R_3 = 0.75 R_2 + 5{}000

and round to the nearest 100.

Calculate the fourth term

R_4

using unrounded

R_3

and round to the nearest hundred.

R_4 = 0.75(53{}750) + 5{}000 = 45{}312.50

, which rounds to

45{}300

Apply

R_4 = 0.75 R_3 + 5{}000

and round to the nearest 100.

Add the four rounded terms together.

80{}000 + 65{}000 + 53{}800 + 45{}300 = 244{}100

Compute total estimated revenue as specified.

Anahtar Kavram

Estimation, Rounding, and Sequences

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