Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Find how many terms of the following series are needed to make the given sum: 5+8+11+14+...=670?

Sagot :

You need 16 more terms not 17 because you already have 4 terms in the series so if you add those 4 terms to the other 16 terms to the series you get a total of 20 terms in total. I hope this helped.
sjustin19963
[tex]670 = n/2[2*5+(n-1)*3][/tex]
[tex]670 = n/2[10+(n-1)*3][/tex]
[tex]1340 = n[10+3n-3][/tex]
[tex]1340 = n[7+3n][/tex]
[tex]1340 = 7n+3n^{2}[/tex]
[tex]3n^{2}+7n-1340 = 0[/tex]
[tex]n^{2}+\frac{7}{3}n-\frac{1340}{3} = 0[/tex]
[tex]n^{2}+\frac{7}{3}n = \frac{1340}{3}[/tex]
[tex]n^{2}+\frac{7}{3}n+\frac{49}{36}[/tex] [tex]=[/tex] [tex]\frac{1340}{3}+\frac{49}{36}[/tex]
[tex]n^{2}+\frac{7}{3}n+\frac{49}{36} = \frac{16129}{36}[/tex]
[tex](n+\frac{7}{6})^2 = \frac{16129}{36}[/tex]
[tex]n+\frac{7}{6} = \sqrt{\frac{16129}{36}}[/tex]
[tex]n = -\frac{7}{6}+\sqrt{\frac{16129}{36}}[/tex]
[tex]n = -1.167 + 21.167[/tex]
[tex]n = 20[/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.