Hey guys I just want to ask what is the formula of
*Arithmetic sequence
*Geometric sequence
*Arithmetic series
*Geometric series
I'm asking for the correct one because I cannot trust google. It has different formulas and I do not know what to believe.
Please help me, this is one of our exam tomorrow thank you. :) - Jesse dinama abledah.
Hello Jesse! I'd be happy to help you with the formulas for arithmetic sequences, geometric sequences, arithmetic series, and geometric series.
Arithmetic Sequence:
An arithmetic sequence is a sequence in which each term is obtained by adding a common difference to the previous term. The formula for the nth term of an arithmetic sequence is given by:
\[a_n = a_1 + (n - 1)d\]
where \(a_n\) represents the nth term, \(a_1\) is the first term, \(n\) is the position of the term in the sequence, and \(d\) is the common difference.
Geometric Sequence:
A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a common ratio. The formula for the nth term of a geometric sequence is given by:
\[a_n = a_1 \cdot r^{(n-1)}\]
where \(a_n\) represents the nth term, \(a_1\) is the first term, \(n\) is the position of the term in the sequence, and \(r\) is the common ratio.
Arithmetic Series:
An arithmetic series is the sum of the terms in an arithmetic sequence. The formula for the sum of the first \(n\) terms of an arithmetic series is given by:
\[S_n = \frac{n}{2}(a_1 + a_n)\]
where \(S_n\) represents the sum of the first \(n\) terms, \(a_1\) is the first term, \(a_n\) is the nth term, and \(n\) is the number of terms in the series.
Geometric Series:
A geometric series is the sum of the terms in a geometric sequence. The formula for the sum of the first \(n\) terms of a geometric series (if \(|r| < 1\)) is given by:
\[S_n = \frac{a_1(1-r^n)}{1-r}\]
where \(S_n\) represents the sum of the first \(n\) terms, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the number of terms in the series.
These formulas should help you in solving problems related to arithmetic and geometric sequences as well as arithmetic and geometric series. Good luck with your exam!