Please help with the below:
Find an expression for the nth term of the given sequence.
a). 3,6, 12,24, ...
b). 151,142,133,124, ...
(a) should be easy -- each term is twice as big
Tn = 3/2 * 2^n
(b) each term is 9 less, so
Tn = 160-9n
Thank you.
To find an expression for the nth term of a given sequence, we need to look for a pattern in the sequence. Let's analyze each sequence separately:
a) 3, 6, 12, 24, ...
Looking at the sequence, we can see that each term is obtained by doubling the previous term. The pattern can be expressed as:
nth term = 3 * 2^(n-1)
For example, the 1st term is 3 * 2^(1-1) which gives us 3 * 2^0 = 3 * 1 = 3. Similarly, the 2nd term is 3 * 2^(2-1) = 3 * 2^1 = 6, and so on.
b) 151, 142, 133, 124, ...
Analyzing this sequence, we can observe that each term is obtained by subtracting 9 from the previous term. The pattern can be described as:
nth term = 151 - 9(n-1)
Using this pattern, we can find any term of the sequence by substituting the value of n into the expression. For example, the 1st term is 151 - 9(1-1) = 151 - 9(0) = 151, the 2nd term is 151 - 9(2-1) = 151 - 9(1) = 142, and so on.
By finding the pattern in each sequence, we have obtained the expressions for the nth term:
a) nth term = 3 * 2^(n-1)
b) nth term = 151 - 9(n-1)