Question

What is the sum of the first 19 terms of an arithmetic series with a rate of increase of 7 and a7 = 46?

1,197
1,273
1,373
1,423
1,327

Answer 1

http://openstudy.com/study#/updates/51e54249e4b08833fb236305

Answer 2

since the general formula for the n-th term is:
\[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\]
where d is constant of your sequance, namely d=7, then we can write:
\[\Large \begin{gathered}
{a_7} = {a_1} + \left( {7 - 1} \right) \times 7 \hfill \\
\hfill \\
46 = {a_1} + \left( {7 - 1} \right) \times 7 \hfill \\
\end{gathered} \]
please solve for a_1

Answer 3

hint:
\[\Large 46 = {a_1} + 42\]

Answer 4

after that we have to compute a_19, using the same general formula above:
\[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\]
so we have:
\[\Large {a_{19}} = {a_1} + \left( {19 - 1} \right) \times 7 = ...?\]

Answer 5

then the requested sum S is given by the subsequent formula:
\[\Large S = \frac{{{a_1} + {a_{19}}}}{2} \times 19 = ...?\]

Answer 6

I got it!! Thank you!

Answer 7

thanks! :)