How would you find the sum of the arithmetic series -77-70-63...+252

Question

I don't understand how to find the sum if I don't know what term the last one (252)? How would I determine which term this is (t of ?=252)

Answer 1

 

First, find the equation for the arithmetic series.

 

  a₁ =-77

  d = +7 .. the common difference

 

a_n = a₁ + (n - 1)d

    = -77 + (n -1)7

    = -77 + 7n - 7  

    = 7n - 84   ... this is the equation for the nth term of the series

 

Use the above equation to find the value of n ... the term number

 

252 = 7n - 84

336 = 7n

    n = 48

 

so 252 is the 48th term  ... use that value in the equation for finding the sum of the first n terms.