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Mathematics 21 Online
OpenStudy (unbelievabledreams):

Help :(

OpenStudy (anonymous):

whats ur question?

OpenStudy (anonymous):

tell your question

OpenStudy (unbelievabledreams):

What is the sum of a 6–term geometric series if the first term is 19 and the last term is 319,333? 372,552 392,160 411,768 431,376

OpenStudy (anonymous):

hmmm sorry iv never done that

OpenStudy (solomonzelman):

last term is the sixth term. You have to find 4 geometric means. lets write that \(\LARGE\color{blue}{ \bf t_1 \times r = t_2 }\) \(\LARGE\color{blue}{ \bf t_1 \times r^{2} = t_3 }\) \(\LARGE\color{blue}{ \bf t_1 \times r^{3} = t_3 }\) See why? \(\LARGE\color{blue}{ \bf t_6 \div r^{ } = t_5 }\) \(\LARGE\color{blue}{ \bf t_6 \div r^{2} = t_4 }\) \(\LARGE\color{blue}{ \bf t_6 \div r^{3} = t_3 }\) See why? I am demonstrating the relationship here... So, if I say \(\LARGE\color{blue}{ \bf t_1 \times r^{3} = t_6 \div r^{3} }\) then, can you solve for r? (this won't be the final answer) (not yet...)

OpenStudy (solomonzelman):

You know the t1 and t6, so you can do it.

OpenStudy (unbelievabledreams):

Thank you. <3

OpenStudy (solomonzelman):

Can you solve for the ratio for me please and show your work. If you want to farther work to make sure you leave with correct answer. I would prefer you to do this, but you don't have to if you don't want to.

OpenStudy (unbelievabledreams):

So it will be 19 x r^3 = 319, 333/r^3

OpenStudy (solomonzelman):

I made a mistake, sorry.

OpenStudy (solomonzelman):

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