Question

the product of 10th‚12th‚14th‚and 16th terms of G.P is 1296. find the 13th term.​

Answer 1

Answer:

6

Step-by-step explanation:

Given-----> Product of 10th , 12th , 14th and 16th terms of GP is 1296 .

To find-----> Find the 13th term

Solution-----> Let first term and common ratio of given GP be a and r .

We know that, formula of nth term of GP is

aₙ = a rⁿ⁻¹

=> a₁₀ = a r¹⁰ ⁻¹

=> a₁₀ = a r⁹

a₁₂ = a r¹²⁻¹

= ar¹¹

a₁₄ = a r¹⁴⁻¹

= a r¹³

a₁₆ = a r¹⁶⁻¹

= a r¹⁵

Now , ATQ,

a₁₀ × a₁₂ × a₁₄ × a₁₆ = 1296

=> a r⁹ × a r¹¹ × a r¹³ × a r¹⁵ = 1296

=> a⁴ r⁹⁺ ¹¹ ⁺¹³ ⁺ ¹⁵ = 1296

=> a⁴ r⁴⁸ = 1296

=> ( a )⁴ ( r¹² )⁴ = 6 × 6 × 6 × 6

=> ( a r¹² )⁴ = 6⁴

=> a r¹² = 6

=> a r¹³⁻¹ = 6

=> a₁₃ = 6