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

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 = ; |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