What is this sequence:/
4,8,20,56,164
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Step-by-step explanation:
Find the formula for the n-th term in the sequence: 4, 12, 20, 28, 36,...
To add from 4 to 12, I'd have to use 8. To add from 12 to 20, I'd also have to use 8. Let's check to see if "add 8" is the rule:
4 + 8 = 12
12 + 8 = 20
20 + 8 = 28
28 + 8 = 36
It appears that the rule is "add 8". So what is the rule for the n-th term? Let's look at the terms:
n = 1: 4
n = 2: 4 + 8
n = 3: 4 + 8 + 8 = 4 + 2×8
n = 4: 4 + 8 + 8 + 8 = 4 + 3×8
n = 5: 4 + 8 + 8 + 8 + 8 = 4 + 4×8
Following this pattern, the rule for the n-th term will be:
an = 4 + (n – 1)8
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