Question

Consider a geometric sequence who third term is 9 and whose sixth term is -8/3. What is the first term? QUICKLY PLEASE!

Answer 1

• 81/4

Explanation:

Given

Geometric sequence with:

• a₃ = 9
• a₆ = -8/3

To find

• The first term a₁

Solution

Formula for nth term is:

• aₙ = a₁rⁿ⁻¹

For the given terms we have:

• a₃ = a₁r² and
• a₆ = a₁r⁵

Comparing the terms:

• a₆/a₃ = r³

Substituting values to find the value of r:

• -8/3 : 9 = -8/27 = (-2/3)³
• r³ = (-2/3)³
• r = -2/3

Then finding a₁:

• a₁(-2/3)² = 9
• a₁(4/9) = 9
• a₁ = 81/4