SOLUTION: The first and the last term of an arithmetic progression are -0.5 and 140.5 respectively. If the number of terms in the sequence is 48, find it's common difference

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Question 1204114: The first and the last term of an arithmetic progression are -0.5 and 140.5 respectively. If the number of terms in the sequence is 48, find it's common difference
Found 4 solutions by math_tutor2020, greenestamps, Edwin McCravy, MathTherapy:
Answer by math_tutor2020(3817) About Me  (Show Source):
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a%5B1%5D = first term = -0.5
a%5B48%5D = 48th term = 140.5
a%5Bn%5D = nth term
n = number of terms = 48
d = common difference

a%5Bn%5D+=+a%5B1%5D+%2B+d%28n-1%29

a%5Bn%5D+=+-0.5+%2B+d%28n-1%29

a%5B48%5D+=+-0.5+%2B+d%2848-1%29

140.5+=+-0.5+%2B+d%2847%29

140.5+=+-0.5+%2B+47d

47d-0.5+=+140.5

47d+=+140.5%2B0.5

47d+=+141

d+=+141%2F47

d+=+3 is the common difference

Answer by greenestamps(13200) About Me  (Show Source):
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Informally....

The difference between the first and last terms is 140.5-(-.5) = 141.

There are 48 terms in the sequence, which means the last term is 47 terms after the first.

The common difference in the sequence is then 141/47 = 3.

ANSWER: 3

Answer by Edwin McCravy(20056) About Me  (Show Source):
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As an enrichment fact, to show a connection between things learned
separately in algebra:

It's also the slope of the line through (1,-0.5) and (48,140.5)

m%22%22=%22%22%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m%22%22=%22%22%28140.5-%28-0.5%29%29%2F%2848-1%29

m%22%22=%22%22%28140.5%2B0.5%29%2F%2847%29

m%22%22=%22%22%28141%29%2F%2847%29

m%22%22=%22%223

Edwin

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The first and the last term of an arithmetic progression are -0.5 and 140.5 respectively. If the number of terms in the sequence is 48, find it's common difference 

Common difference (d) =