Question 1023561
General term, {{{44+(-4)(n-1)}}}
{{{44-4n+4}}}
{{{48-4n}}}


Apply the summation formula for arithmetic progression
{{{(48+44-4n)(n/2)=260}}}


{{{(24+22-2n)n=260}}}
{{{(46-2n)n=260}}}
{{{(23-n)n=130}}}
{{{-n^2+23n-130=0}}}
{{{n^2-23n+130=0}}}


{{{n=(23+- sqrt(23^2-4*130))/2}}}

{{{n=(23+- sqrt(9))/2}}}

{{{n=(23+- 3)/2}}}

n is either 10  or  13;
but they cannot both be correct.


CHECK WHICH n value:
10?
48-4n
48-4*10
8
Last row would have 8 pieces.
13?
48-4*13
48-52
-4
Last row would not be able to have NEGATIVE FOUR pieces.


Correct answer is n=10.