# What is the 7th term of the geometric sequence 4, -20, 100, …?

$7$ th term is $62500$
$n$ th term of geometric sequence is T_n= a*r^(n-1); a,r,n are the first term , common ratio and requred term respectively.
Here $a = 4 , r = - \frac{20}{4} = \frac{100}{-} 20 = - 5 , n = 7 \therefore {T}_{7} = 4 \cdot {\left(- 5\right)}^{7 - 1}$ or
${T}_{7} = 4 \cdot {\left(- 5\right)}^{6} = 62500$ [Ans]