crispingolfer7082
18.12.2019 •
Mathematics
How do you find both the 1st term of an arithmetic sequence and the common difference?
for example, when the seventh term in the sequence is 5 and the sum of the first 16 terms is 20
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Ответ:
An arithmetic sequence is one in which consecutive terms differ by some fixed number. Recursively, such a sequence is given by
where is the common difference between terms.
Using this definition, you can express any term of the sequence in terms of , since
and so on down to the explicit rule,
The sum of the first terms, , of such a sequence is
or, using the explicit rule,
Now, given and , we have
which you can solve to get
Ответ: