In geometric sequence tn, find S15 if t3=8 , t5=32 and t8 < 0.

Answer 1

t₃ = 8, t₄ = 8r_, t₅ = 8r² = 32

So, r² = 4. r = 2 or -2. Since t₈ < 0, r must be negative.

t₃ = t₂r = -2t₂ = 8. So, t₂ = -4.

t₂ = t₁r = -2t₁ = -4. So, t₁ = 2.

S₁₅ = [t₁(1 - r¹⁵)] / (1 - r) = 2(1 - (-2)¹⁵) / (1 - (-2)) = 21846