Question 782245
Hi I need help finding the first term of an Arithmetic Series with the given info.

My common difference is 6 
My Sn is 574 
My N is 14

The answer according to my text book is 2 can you help me? 


The sum of an arithmetic series is: {{{S[n] = (n/2)(2a[1] + (n - 1)d)}}}, with:


{{{S[n]}}} given as: 574; {{{n}}} given as: 14; {{{a[1]}}} NOT GIVEN; and {{{d}}}, or common difference given as: 6


Therefore, {{{S[n] = (n/2)(2a[1] + (n - 1)d)}}} becomes: {{{574 = (14/2)(2a[1] + (14 - 1)6)}}}


{{{574 = 7(2a[1] + (13)6)}}}


{{{574 = 7(2a[1] + 78)}}}


{{{574 = 14a[1] + 546}}}


{{{14a[1] = 574 - 546}}}

{{{14a[1] = 28}}}


The 1st term, or {{{a[1]}}} = {{{28/14}}}, or {{{highlight_green(2)}}}