the first term of a geometric progression is 81 and the common ratio is 2/6. the product of the first 10 terms is
Answers
Answer:
5
Step-by-step explanation:
5
Given : the first term of a geometric progression is 81 and the common ratio is 2/6.
To Find : the product of the first 10 terms
Solution:
First term a = 81
r = common ratio = 2/6 = 1/3
nth term = arⁿ⁻¹
GP 10 terms
a , ar , ar² , _____ , ar⁹
Product = a¹⁰r¹⁺²⁺³ ... ⁺⁸⁺⁹
1 + 2 + 3 + .. + 8 + 9 = 9 (10)2 = 45
Product = a¹⁰r⁴⁵
a = 81 = 3⁴
r = 1/3
= (3⁴)¹⁰(1/3)⁴⁵
= 3⁴⁰/3⁴⁵
= 1/3⁵
= 1/243
Product of the first 10 terms is 1/243
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