The third term of G.P. is 4. The product of its first 5 terms is(A) 43

1.	The third term of G.P. is 4. The product of its first 5 terms is(A) 43 (B) 44 (C) 45 (D) None of these
Answer» (C) 4⁵ Explanation: Given third term of G.P, T₃ = 4 To find Product of first five terms We know that, T_n = a r^{n – 1} It is given that, T₃ = 4 ⇒ ar^{3 – 1} = 4 ⇒ ar² = 4 … (i) Product of first 5 terms = a × ar × ar² × ar³ × ar⁴ = a⁵r^1+2+3+4 = a⁵r¹⁰ = (ar²)⁵ = (4)⁵ [from (i)] Hence, the correct option is (C)

The third term of G.P. is 4. The product of its first 5 terms is(A) 43 (B) 44 (C) 45 (D) None of these

Answer»

(C) 4⁵

Explanation:

Given third term of G.P, T₃ = 4

To find Product of first five terms

We know that,

T_n = a r^{n – 1}

It is given that, T₃ = 4

⇒ ar^{3 – 1} = 4

⇒ ar² = 4 … (i)

Product of first 5 terms = a × ar × ar² × ar³ × ar⁴

= a⁵r^1+2+3+4

= a⁵r¹⁰

= (ar²)⁵

= (4)⁵ [from (i)]

Hence, the correct option is (C)