Question

given question is from GP

Answer 1

Answer:

a = 2, n = 6.

Step-by-step explanation:

Let a , ar ,  ar², ar³,......, arⁿ  be in GP.

Let a be the first term of the GP and aₙ be the last term of the GP.

Common ratio r = 3.

aₙ = arⁿ⁻¹ = 486

=> arⁿ/r = 486

=> arⁿ  = 486 * r

=> arⁿ = 486 * 3 = 1458.

Sum to n terms of GP , Sₙ = a (rⁿ - 1) / r - 1 = 728

=> 728 = a(rⁿ - 1 )/ r - 1

=> 728 = arⁿ - a / r - 1

=> 728 = 1458 - a / 3 - 1

=> 728 * 2 =  1458 - a

=> a = 1458 - 1456

=> a = 2.

We know that aₙ = arⁿ⁻¹

=> 486 = 2 (3)ⁿ⁻¹

=> 3ⁿ⁻¹ = 243

=> 3ⁿ⁻¹ = 3⁵

//We know that in exponents, when bases are same powers are equal.

=> n - 1 = 5

=> n = 6.