Assuming that each of the given geometric sequence is a pyramid networking. Find the total number of members in each sequence. 1.5, 15, 45, 135, 405, 12152.2,8,32,...,8192
Answer (1)
Sequences:5, 15, 45, 135, 405, 12152, 8, 32, ..., 81921st Sequence: 5, 15, 45, 135, 405, 1215Step-by-step:This is a geometric sequence.Common ratio (r): 15 ÷ 5 = 3Terms: 6 terms total.To find total number of members:Add all terms:5 + 15 + 45 + 135 + 405 + 1215 = 1820 members2nd Sequence: 2, 8, 32, ..., 8192Step-by-step:This is also a geometric sequence.Common ratio (r): 8 ÷ 2 = 4First term (a): 2Last term: 8192Use formula to find number of terms:a * r^(n-1) = 81922 * 4^(n-1) = 8192Divide both sides by 2:4^(n-1) = 4096Now, find power of 4 that gives 4096:4^6 = 4096 → so n-1 = 6 → n = 7 termsNow add all 7 terms:2 + 8 + 32 + 128 + 512 + 2048 + 8192 = 10,922 membersFinal Answers:1st sequence: 1,820 members2nd sequence: 10,922 members
