Question

4m + 1, m + 1 and 10 - m are the first three terms of a geometric sequence. Find t4.

Answer 1

to be an GS
(m+1)/(4m+1) = (10-m)/(m+1)
cross-multiply
m^2 + 2m + 1 = 10 +39m - 4m^2
5m^2 - 37m -9 = 0

m = (37 ± √1549)/10

you don't state whether you want "exact" values or if you want the fourth term in terms of m

you could simply say ...

since the common ratio is (m+1)/(4m+1)
term(4) = r (term(3) )
= (10-m)(m+1)/(4m+1)