What is the value of \(5+4\cdot 5+4\cdot 5^2+4\cdot 5^3+4\cdot 5^4+4\cdot 5^5?\)

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What is the value of \(5+4\cdot 5+4\cdot 5^2+4\cdot 5^3+4\cdot 5^4+4\cdot 5^5?\)

A. \(5^6\)
B. \(5^7\)
C. \(5^8\)
D. \(5^9\)
E. \(5^{10}\)

Answer: A

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Let expression = S.

S/5 = 1+4+4*5+4*5^2+4*5^3+4*5^4
which equals

S-4*5^5

So, S/5 = S- 4*5^5.

S-S/5= 4*5^5

4/5S = 4*5^5

S= (5/4)*4*5^5= 5*5^5=[spoiler]5^6,A[/spoiler]

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Gmat_mission wrote:
Sun Nov 28, 2021 6:51 am
What is the value of \(5+4\cdot 5+4\cdot 5^2+4\cdot 5^3+4\cdot 5^4+4\cdot 5^5?\)
You can also replace "4" with "5 - 1", so the expression becomes

5 + (5-1)*5 + (5-1)*5^2 + (5-1)*5^3 + (5-1)*5^4 + (5-1)*5^5
= 5 - 5 + 5^2 - 5^2 + 5^3 - 5^3 + 5^4 - 5^4 + 5^5 - 5^5 + 5^6
= 5^6
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