Question 647305
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
the sum of the first fifteen terms of an arithmetic terms progression is 270. 
find the first term and the common difference if the the fifteenth terms is 39
{{{S[n]=(n(a[1]+a[n]))/2}}} &#8658; {{{(15/2)(a[1] + 39) = 270}}}, {{{a[1] = 36-39}}} = -3
{{{a[n]=a[1]+(n-1)*d}}}  &#8658; {{{-3 + 14d = 39}}}&#8658; {{{14d = 42}}} d = 3
and
{{{a[15] = -3 + 14*3 = 39}}}