Question

the sum of the second and the fifth term of an AP is 8 and that of the third and seventh is 14.find the eleventh term

Answer 1

\(a_2 +a_5=8\)
\(a_3+a_7=14\)

ok could you tell whats the \(a_n\) term in any AP ?

Answer 2

a(n)=a+(n-1)d

Answer 3

thus
\(a_2=a_0+d\)
\(a_5=a_0+4d\)
\(a_0+d+a_0+4d=8\)
\(2a_0+5d=8....eq (1)\)

\(a_3=a_0+2d\)
\(a_7=a_0+6d\)
\(a_0+2d+a_0+6d=14\)
\(2a_0+7d=14....eq (2)\)


solve eq 1 and 2 for \(a_0\) and d