Explicit and Recursive Formulas for Geometric Sequences
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- (Video) A Formula for the nthn^{\text{th}}nth Term by PatrickJMT This video by PatrickJMT covers formulas to find the nnnth term of a sequence. Summary\large{\text{Summary}}Summ…
By Stefan Cuevas, Alex Federspiel, Jonathan Heller, Caroline K, Anusha Rahman
- আমরা গুণোত্তর সিকুয়েন্স নিয়ে আলোচনা করেছি। এখন আমরা গুণোত্তর সিকুয়েন্সের যেকোন পদ নির্ণয়ের সূত্র বের করব। এখানে, সিকুয়েন্সটার সাধারণ অনুপাত 333। অর্থাৎ যেকোন পদকে 333 দিয়ে গুণ ক…
By Pritom Kundu · বাংলা
- Two Ways to Represent Geometric Sequences \\ Writing out the sequence takes up a lot of space and requires people to figure out the pattern. There are better, more concise ways …
By Christine, Alex Federspiel, Jonathan Heller, Anusha Rahman, Caroline K
- Maximum Depth Exceeded: Fun with Sequences and Python, Part 5 To see the previous part of this story, go here. An example of a recursive formula for a geometric sequence is bn=3…
By Joshua Siktar, Caroline K
Problems 22
- If a geometric sequence has a common ratio of 444 and starts at a1=1a_{1} = 1a1=1, what is the recursive form of ana_nan?
- If a geometric sequence has a common ratio of 777 and starts at a1=1a_{1} = 1a1=1, what is the explicit form of ana_nan?
- Find the recursive formula for 0.3,0.03,0.003,0.0003,⋯0.3,0.03,0.003,0.0003, \cdots0.3,0.03,0.003,0.0003,⋯
- A geometric sequence with a1=20a_{1} = 20a1=20 and a2=10a_{2} = 10a2=10 has an explicit formula, an=C⋅Rn−1,a_n = C\cdot R^{n-1},an=C⋅Rn−1, for some constants CCC and RRR. Fin…
- If a geometric sequence has a common ratio of 555 and starts at a1=2a_{1} = 2a1=2, what is the recursive form of ana_nan?
- If a geometric sequence has a common ratio of 555 and starts at a1=2a_{1} = 2a1=2, what is the explicit form of ana_nan?
- Which function represents the following geometric sequence? 1,2,4,8,16,…1,2,4,8,16,\dots1,2,4,8,16,… (Assume the sequence starts when n=1n=1n=1, so a1=1a_1 = 1a1=1.)
- Find the explicit formula for the sequence. 1,13,19,127,181,...1,\frac{1}{3},\frac{1}{9},\frac{1}{27},\frac{1}{81},...1,31,91,271,811,... (Assume the sequence starts with n=…
- Let SSS be a subset of the integers 1,2,…,1001,2,\dots,1001,2,…,100 such that 3x∉S3x\notin S3x∈/S whenever x∈Sx\in Sx∈S. What is the largest possible size of SSS? (Hint: Conside…
- Suppose that a geometric sequence has a5=120a_5 = 120a5=120 and a8=3240a_8 = 3240a8=3240. What is the common ratio of the geometric sequence?
- Which of these is a geometric sequence in recursive form?
- Which of these is a geometric sequence in explicit form?
- Which of these is a geometric sequence in recursive form?
- Which of these is a geometric sequence in recursive form?
- If a geometric sequence has a common ratio of 555 and starts at a1=1a_{1} = 1a1=1, what is the recursive form of ana_nan?
- If a geometric sequence has a common ratio of 161616 and starts at a1=6a_{1} = 6a1=6, what is the recursive form of ana_nan?
- What is the recursive formula of the sequence 1,2,4,8,16,…1, 2, 4, 8, 16, \dots1,2,4,8,16,…?
- What is the recursive formula of the sequence 8,4,2,1,12,…8, 4, 2, 1, \frac{1}{2}, \dots8,4,2,1,21,…?
- What is the recursive formula of the sequence 123456,12345.6,1234.56,123.456,12.3456…?123456, 12345.6, 1234.56, 123.456, 12.3456\dots?123456,12345.6,1234.56,123.456,12.3456…?
- Which function represents the following geometric sequence? 12,14,18,116…\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16} \dots21,41,81,161… (Assume the sequence starts w…
- Find the explicit formula for the geometric sequence. 128,64,32,16,8,4,…128, 64, 32, 16, 8, 4, \dots128,64,32,16,8,4,…
- Which function represents the following sequence? 4,8,16,32,…4,8,16,32,\dots4,8,16,32,…