## anonymous one year ago 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

1. anonymous
2. Michele_Laino

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

3. Michele_Laino

hint: $\Large 46 = {a_1} + 42$

4. Michele_Laino

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: $\Large {a_{19}} = {a_1} + \left( {19 - 1} \right) \times 7 = ...?$

5. Michele_Laino

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

6. anonymous

I got it!! Thank you!

7. Michele_Laino

thanks! :)