The third term of a GP is 3. What is the product of the first five terms?a)216b)226c)243d)Cannot be determined due to insufficient dataCorrect answer is option 'C'. Can you explain this answer?

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ACT Exam > ACT Questions > The third term of a GP is 3. What is the prod...

The third term of a GP is 3. What is the product of the first five terms?

a)
216
b)
226
c)
243
d)
Cannot be determined due to insufficient data

Correct answer is option 'C'. Can you explain this answer?

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Verified Answer

The third term of a GP is 3. What is the product of the first five ter...

Concepts:
Let us consider sequence a₁, a₂, a₃ …. a_n is an G.P.

Common ratio = r =
n^th term of the G.P. is an = arⁿ⁻¹
Sum of n terms = s = ; where r >1
Sum of n terms = s =; where r <1
Sum of infinite GP = s_∞= |r| < 1

Where a is 1^st term and r is common ratio.

Calculation:
Given: The third term of a GP is 3
Let 'a' be the first term and 'r' be the common ratio.
∴ T₃ = ar² = 3
We know that T_n = a r^n-1
So, T₁ = a, T₂ = ar, T₃ = ar², T₄ = ar³, T₅ = ar⁴
Now, Product of the first five terms = a × ar × ar² × ar³ × ar⁴ = a⁵r¹⁰ = (ar²)⁵ = 3⁵ = 243

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