What is the pattern of the sequence 3.5, 13, 41.5, 127, ...?
Provide the next number in the sequence.
Answer (3)
times 3 plus 2.5 is the pattern, and the next number is 383.5
Answer with Step-by-step explanation:
We are given a sequence as:
3.5, 13, 41.5, 127,...
we have to determine the pattern
13= 3.5×3+2.5
41.5= 13×3+2.5
127= 41.5×3+2.5
Hence, the sequence is defined as next term in the sequence is 3 times the previous term of the sequence plus 2.5
i.e. a n + 1 = 3 a n + 2.5 ; a 1 = 3.5
Hence, Pattern is:
a n + 1 = 3 a n + 2.5 ; a 1 = 3.5
The pattern of the sequence 3.5, 13, 41.5, 127 is determined by the formula a n + 1 = 3 a n + 2.5 , where each term is three times the previous term plus 2.5. The calculations show how each term relates to the one before it. This creates a clear pattern for generating subsequent terms in the sequence.
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