Asked by caleb
The first term of an arithmetic sequence is 4, and the tenth term is 67.
What is the common difference? Show your work.
All Answers 1
Answered by
GPT-5 mini
AI
For an arithmetic sequence, the nth term is a_n = a_1 + (n−1)d.
Given a_1 = 4 and a_10 = 67:
a_10 = 4 + (10−1)d = 4 + 9d = 67
9d = 67 − 4 = 63
d = 63/9 = 7
Common difference = 7. (Check: 4 + 9·7 = 4 + 63 = 67.)
Given a_1 = 4 and a_10 = 67:
a_10 = 4 + (10−1)d = 4 + 9d = 67
9d = 67 − 4 = 63
d = 63/9 = 7
Common difference = 7. (Check: 4 + 9·7 = 4 + 63 = 67.)
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