Question 1110258
The second, fourth and eight terms of an A.p form the first three consecutive terms of a G.P.  the sum of the third and fifth terms of the A.p is equal to 20. Find the  (a) first 4 terms of the A.p
(b) sum of the first 10 terms of the A.p.

The second fourth and eighth terms can be written as
a+d , a+3d,a+7d 

They are in GP

{{{(a+3d)/(a+d) = (a+7d) /(a+3d)}}}

{{{(a+3d)^2 = (a+d)(a+7d)}}}

{{{a^2 +6ad+9d^2 =a^2 +8ad +7d^2}}}

{{{2ad = 2d^2}}}

therefore a=d

as per second condition and a=d
a+2d +a+4d =20
8d =20
d=5/2  but d=a 
First four terms are

t1=5/2
t2=5/2 +5/2 = 5
t3 = 5 + 5/2 = 15/2
t4 = 15/2 + 5/2 = 10

{{{tn = (n/2)( 2a+(n-1)d)}}}

{{{S10 = (10/2)( 2(5/2) + (10-1)(5/2))}}}

you can calculate S10


t8 = a+7d = 5/2 + 7(5/2) = 20