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Algebra Level 2

3 + 3 2 + 3 3 + 3 4 + 3 5 + 3 6 + 3 7 = ? \large 3+3^2+3^3+3^4+3^5+3^6+3^7 = \ ?


The answer is 3279.

Ramiel To-ong by Ramiel To-ong , 37, Philippines

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3 solutions

Mahdi Raza
Jun 7, 2020

The terms form a G.P. whose sum will be:

= a ( r n − 1 ) r − 1 = 3 ( 3 7 − 1 ) 3 − 1 = 3279 \begin{aligned} &= \dfrac{a(r^n - 1)}{r -1} \\ \\ &= \dfrac{3(3^7 - 1)}{3-1} \\ \\ &= \boxed{3279} \end{aligned}

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Mahdi I can't understand "\[\begin{align} &= \dfrac{a(r^n - 1)}{r -1} \\ \\ &= \dfrac{3(3^7 - 1)}{3-1} \\ \\ &= \boxed{3279}

\end{align}\]"

SRIJAN Singh - 8 months, 2 weeks ago

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I think this has been an error for many solutions where I have used Latex. There is an extra line in between that might be causing the problem. I need to fix it. Thanks

Mahdi Raza - 8 months, 2 weeks ago

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Yeah! btw thanks.

SRIJAN Singh - 8 months, 2 weeks ago
Panya Chunnanonda
Oct 15, 2015

(x- 1)(1+ x+ x^2+ x^3+ x^4+...x^n)= (x^n+1)- 1

so

3(1+ 3+ 3^2+ 3^3+ 3^4+ 3^5+ 3^6)= 3 ( 3^7- 1)/ (3-1) = 3 ( 2187- 1)/ 2= 3279

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Ramiel To-ong
Oct 6, 2015

The sum = 3 + 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 + 3^7 = 3279 or we could simply use the summation formula

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