asked 234k views
5 votes
Find the 6th term of a geometric sequence with t1 = 7 and t9 = 45,927.

asked
User Weima
by
8.6k points

1 Answer

2 votes
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 = ar⁵ = 7*3⁵ = 1701

Sixth term = 1701
answered
User Nothingness
by
7.8k points
Welcome to Qamnty — a place to ask, share, and grow together. Join our community and get real answers from real people.