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An arithmetic progression has a first term of 160 and a common difference of -8. What is the general term and the 8th term?
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Step-by-step solution
5 stepsAnalyze the given sequence and identify the pattern.
The sequence of systolic BP readings is .
Let's find the differences between consecutive terms:
The differences are not constant, so the sequence as written is not a standard arithmetic progression. However, given the context of arithmetic progressions, it is highly probable that there is a typo in the sequence. The common difference appears to be for most terms. We will assume the sequence is an arithmetic progression with a common difference of , meaning the third term 148 would ideally be 144 to fit this pattern.Identify the first term and common difference.
Based on our assumption, the first term is .
The common difference is .Write the general term for the arithmetic progression.
The formula for the -th term of an arithmetic progression is .
Substitute and :Simplify the general term.
The general term is .
Predict the BP after 8 hours.
The question asks for the BP after 8 hours, which corresponds to the 8th term () in the sequence.
Substitute into the general term formula:The predicted BP after 8 hours is .
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