the second term of a geometric sequence is 18 and the fourth term is 8 find the common ratio . And find the sum of the first 6 terms
Accepted Solution
A:
Answer:ratio: 2/3sum: 73 8/9Step-by-step explanation:The general term of a geometric sequence is ... an = a1·r^(n-1)You have the 2nd and 4th terms, so ... a2 = a1·r^(2-1) = a1·r a4 = a1·r^(4-1) = a1·r^3We can find r from the ratio ... a4/a2 = (a1·r^3)/(a1·r) = r^2 = 8/18 = 4/9Then r is ... r = √(4/9) = 2/3 . . . . the common ratioThe first term is ... a2 = 18 = a1·(2/3) a1 = (3/2)·18 = 27__The sum of the first 6 terms is ... Sn = a1·(r^n -1)/(r -1) S6 = 27·((2/3)^6 -1)/(2/3 -1) S6 = 27·(64/729-1)/(2/3-1) = (27)(665)/243 = 73 8/9The sum of the first 6 terms is 73 8/9._____Check on the sumThe first 6 terms are ... 27, 18, 12, 8, 5 1/3, 3 5/9Their sum is 73 8/9, as above.