Answered

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

Verified Answer :

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

\(670 = n/2[2*5+(n-1)*3]\)
\(670 = n/2[10+(n-1)*3]\)
\(1340 = n[10+3n-3]\)
\(1340 = n[7+3n]\)
\(1340 = 7n+3n^{2}\)
\(3n^{2}+7n-1340 = 0\)
\(n^{2}+\frac{7}{3}n-\frac{1340}{3} = 0\)
\(n^{2}+\frac{7}{3}n = \frac{1340}{3}\)
\(n^{2}+\frac{7}{3}n+\frac{49}{36}\) \(=\) \(\frac{1340}{3}+\frac{49}{36}\)
\(n^{2}+\frac{7}{3}n+\frac{49}{36} = \frac{16129}{36}\)
\((n+\frac{7}{6})^2 = \frac{16129}{36}\)
\(n+\frac{7}{6} = \sqrt{\frac{16129}{36}}\)
\(n = -\frac{7}{6}+\sqrt{\frac{16129}{36}}\)
\(n = -1.167 + 21.167\)
\(n = 20\)

Related Questions