Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.