Calculate the sum of first 45 numbers

Question

Calculate the arithmetical sum of first 45 numbers, where $a_n= (1-\sqrt3)n+2\sqrt3$.

I tried with all the formulas, but it seemes that none really work...

Answer 1

You can simply take the series as an arithmetic progession and solve. Answer, in my opinion is: 45*(23 - 21√3) PS: As far as I have understood, you wanted the sum of first 45 TERMS of this series, right?

Answer 2

Hint:

An arithmetic sequence is linear, so that the average of the terms is equal to the average of the extreme terms. The sum easily follows.