Find the 6th term of a geometric sequence with t1 = 7 and t9 = 45,927.

GS = a rⁿ ⁻ ¹

t₁ = 7, a = 7

t₉ = 45927 ar⁹ ⁻ ¹ = ar⁸ = 45927

a = 7 ... (a)

ar⁸ = 45927 ... (b)

Equation (b) : (a)

ar⁸/a = 45927/7

r⁸ = 6561

Take the eight root of both sides

⁸√r⁸ = ⁸√6561

r = 3

Sixth term = ar⁶ ⁻ ¹ = ar ⁵ = 7*3⁵ = 1701

Sixth term = 1701