Question

100 Points! Algebra question. Photo attached. Thank you!

Answer 1

• a₁ = 121.5

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Use the formula for the sum of n terms of a GP:

• Sₙ = a₁(1 - rⁿ) / (1 - r)

And use the nth term formula:

• aₙ = a₁*rⁿ⁻¹ = a₁*rⁿ/r ⇒

• rⁿ = aₙ*r/a₁

We can rearrange the sum formula to solve for the first term:

• Sₙ = a₁(1 - aₙ*r/a₁) / (1 - r) ⇒

• Sₙ = ( a₁ - aₙ*r) / (1 - r)

Plugging in the given values, we get:

• 4860 = (a₁ - 3280.5*3)/(1 - 3)
• 4860 = (a₁ - 9841.5)/ (-2)
• a₁ - 9841.5 = -2*4860
• a₁ - 9841.5 = -9720
• a₁ = 9841.5 - 9720
• a₁ = 121.5

Therefore, the first term of the GP is 121.5.