Activity 3: > Getting To Know Yo, What Is The Nth Term For Each Sequence Below?, 1. 3, 4, 5, 6, 7, ..., 2. 3, 5, 7, 9, 11, ..., 3. 2, 4, 8, 16, 32, ..

Activity 3: > Getting to Know You

What is the nth term for each sequence below?
1. 3, 4, 5, 6, 7, ...
2. 3, 5, 7, 9, 11, ...
3. 2, 4, 8, 16, 32, ...
4. -1, 1, -1, 1, -1, ...
1 1 1 1
5. 1,
2 3 4 5

 

1. 3, 4, 5, 6, 7, ... (Arithmetic sequence)

a_{1} = 3\\ d = 1 \\ a_{n} = a_{1} + (n-1)d \\ a_{n} = 3 + (n-1)1 \\ a_{n} = 3 + (n-1) \\ a_{n} = 3 + n-1 \\ \boxed{\boxed{a_{n} = n + 2}}

2. 3, 5, 7, 9, 11, ... (Arithmetic sequence)

a_{1} = 3\\ d = 2 \\ a_{n} = a_{1} + (n-1)d \\ a_{n} = 3 + (n-1)2 \\ a_{n} = 3 + (2n-2) \\ a_{n} = 3 + 2n - 2\\ \boxed{\boxed{a_{n} = 2n + 1}}

3. 2, 4, 8, 16, 32, ... (Geometric sequence)

a_{1} = 2\\ r = 2 \\ a_{n} = a_{1} r^{n-1} \\ a_{n} = (2) (2)^{n-1} \\ a_{n} = 4^{n-1} \\ \boxed{\boxed{a_{n} = 2^{n} }}

4. -1, 1, -1, 1, -1, ... (Geometric sequence)

a_{1} = -1\\ r = -1 \\ a_{n} = a_{1} r^{n-1} \\ a_{n} = (-1) (-1)^{n-1} \\ a_{n} = 1^{n-1} \\ \boxed{\boxed{a_{n} = -1^{n} }}

5. 1, \frac{1}{2} ,\frac{1}{3} ,\frac{1}{4} ,\frac{1}{5} (Harmonic sequence)

a_{1} = 1 \\ d = 1\\ a_{n} = \frac{1}{a_{1} + (n-1)d} \\a_{n} = \frac{1}{1 + (n-1)1} \\ a_{n} = \frac{1}{1 + (n-1) } \\ a_{n} = \frac{1}{1 + n-1} \\ \boxed{\boxed{a_{n} = \frac{1}{n} }}

For the terminologies used, kindly look for its meanings in the links below if its meaning isnt stated yet.


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