Question 1153525

AP: 
2nd term: {{{a + d}}}, 
4th term: {{{a + 3d}}}, 
8th term: {{{a + 7d}}}

 These {{{3}}} terms are in GP: 

{{{   (a + d)(a + 7d)  -(a + 3d)^2 =0}}}
{{{a^2 + 8 a d + 7 d^2-(a^2 + 6 a d + 9 d^2)=0}}}
{{{a^2 + 8 a d + 7 d^2-a^2 - 6 a d - 9 d^2=0}}}
{{{ 2a d  - 2 d^2=0}}}
 {{{2d(a - d) = 0}}} 
{{{2ad - 2d^2=0 }}}
{{{2ad =2d^2 }}}
 {{{a = d}}}




Sum of 3rd and 5th terms is:
 
{{{(a + 2d) + (a + 4d) =20}}} 
{{{2a + 6d = 20}}}
{{{  8d = 20}}} 
{{{d = 2.5}}} or {{{d=(5/2)}}}

=>{{{ a = 2.5}}}or {{{(5/2)}}}

 AP:
1st term: {{{2.5}}} 
2nd term: {{{5}}} 
3rdterm:{{{7.5}}}
4th term: {{{10}}} 
5thterm:{{{12.5}}} 
8th term: {{{20}}}