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What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6?

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Bunuel
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What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6? [#permalink] New post  02 Apr 2018, 02:23
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What is the value of \(7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6\)?

(A) 6^7
(B) 6^9
(C) 7^7
(D) 7^8
(E) 7^9
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eabhgoy
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Re: What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6? [#permalink] New post  11 Feb 2019, 11:45
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Bunuel wrote:
What is the value of \(7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6\)?

(A) 6^7
(B) 6^9
(C) 7^7
(D) 7^8
(E) 7^9


We can re-write the above equation in terms of 7:

7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6
= 7 + (7-1)*7 + (7-1)*7^2 + (7-1)*7^3 + (7-1)*7^4 + (7-1)*7^5 + (7-1)*7^6
= 7 + 7^2 - 7 + 7^3 - 7^2 + 7^4 - 7^3 + 7^5 - 7^4 + 7^6 - 7^5 + 7^7 - 7^6
= 7^7

Hence C is the correct answer.
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kunalcvrce
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Re: What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6? [#permalink] New post  02 Apr 2018, 02:53
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Bunuel wrote:
What is the value of \(7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6\)?

(A) 6^7
(B) 6^9
(C) 7^7
(D) 7^8
(E) 7^9


Approach one-->simplyfing the eq
7+6(7+......+7^6) inside bracket is in GP so applying formula
7+6*7(7^6-1)/(7-1)=7^7

Option C

Approach two by looking into the options.

The max value can be when when all are equal to 7^6 so overall sum will be 6*7^7(option d,E ignored very big, a,b too small)
only option C will be near this value.
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Bunuel
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Re: What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6? [#permalink] New post  02 Apr 2018, 02:55
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Bunuel wrote:
What is the value of \(7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6\)?

(A) 6^7
(B) 6^9
(C) 7^7
(D) 7^8
(E) 7^9


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What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6? [#permalink] New post  11 Jun 2018, 18:21
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One of the other method we could do this is as follows.
What is the value of 7+6∗7+6∗7^2 +6∗7^3 +6∗7^4 +6∗7^5 +6∗7^6 ?

(A) 6^7
(B) 6^9
(C) 7^7
(D) 7^8
(E) 7^9

By just comparing last digit of question vs answer choices.

question last digits = 7+2+4+8+6+2+4 = 3 (3 would be the last digit of all equation provided)

Looking at answers only (C) gets last digit 3. thus, Answer is (C)
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Re: What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6? [#permalink] New post  11 Feb 2019, 07:38
Bunuel wrote:
What is the value of \(7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6\)?

(A) 6^7
(B) 6^9
(C) 7^7
(D) 7^8
(E) 7^9


So just keep on taking 7 as common from this series

\(7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6\)

7( 1 + 6 + 6 * 7 + 6 * 7^2 + 6*7^3 + 6*7^4 +6*7^5)

So when you keep progressing in this series, you will get

\(7^7\)
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Re: What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6? [#permalink] New post  08 Jun 2019, 13:09
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Bunuel wrote:
What is the value of \(7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6\)?

(A) 6^7
(B) 6^9
(C) 7^7
(D) 7^8
(E) 7^9


Solution



7 + 6(7 + 7^2 …. + 7^6)

Series: (7 + 7^2 …. + 7^6)

b1 = 7; r = 7; n = 6
Sum of n term GP = b1 * (r^n -1)/(r-1)
Sum of series = 7(7^6 - 1)/(7-1) = (7^7 - 7)/6

Total sum = 7 + 6(7^7 - 7)/6 = 7 + 7^7 - 7 = 7^7

ANSWER: C
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Re: What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6? [#permalink] New post  03 Jul 2022, 14:56
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Bunuel wrote:
What is the value of \(7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6\)?

(A) 6^7
(B) 6^9
(C) 7^7
(D) 7^8
(E) 7^9


See attached.

Answer choice C.
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Re: What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6? [#permalink] New post  19 Jul 2023, 23:25
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Re: What is the value of 7 + 6*7 + 6*7^2 + 6*7^3 + 6*7^4 + 6*7^5 + 6*7^6? [#permalink]
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