5 times the 5th term of arthmetic progression is equa to 10 times the 10th term. Find the common difference and the first term

Answer 1

5(a+4d) = 10(a+9d)
5a+20d = 10a+90d
a = -14d

So, there is no unique solution. Some examples are

a = 14
d = -1
14,13,12,11,10,9,8,7,6,5
5*10 = 10*5

a = -7
d = 0.5
-7,-6.6,-6,-5.5,-5,-4.5,-4,-3.5,-3.-2.5
5(-5) = 10(-2.5)