1. Find the sum of the terms of a geometric sequence where the first term is 4, the last term is 324 and the common ratio is 3.2. Find the sum of the five terms of 4,12,36,108,...
Answer (1)
Answer:The sum of the first 5 terms is 484.Step-by-step explanation:1. Find the sum of the terms of a geometric sequence where:First term a=4Last term, l=324Common ratio = 3We first need to determine how many terms, n, there are.Use the formula for the n-th term of a geometric sequence:a(n) = a*3^(n-1)Set a(n) to the last term (324) 324 =4*3^(n-1)Divide both sides by 4: 81 = 3^(n-1) Since 3^4 = 81 We can write 3^4 = 3^(n-1) We can see that 4 = n - 1 n = 5There are five terms in this sequence.The sum of the first five terms can use the relationship: Sn = a*(r^n - 1)/(r- 1) where Sn is the sum of the first n terms. n = 5 a = 4 r = 3 S(5) = 4*(3^5 - 1)/(3 - 1) S(5) = 4*(243 - 1)/(2) S(5) = 4*(242)/(2) S(5) = 4*(121) S(5) = 484The terms are: 4 12 36108324Total = 484
