The 30th term of the given sequence is 175
What is arithmetic sequence ?
Arithmetic sequence is a sequence in which the differences between every consecutive terms are always same.
Example : 3, 5, 7, 9, ..... is an arithmetic sequence where the common difference is 2.
What is the formula of arithmetic sequence ?
Formula of arithmetic sequence is , \(a_{n}\) = \(a_{1}\) + (n-1)d
where \(a_{n}\) = term in the sequence,
\(a_{1}\) = \(1^{st\\}\) term in the sequence,
d = common difference between terms
What is the required 30th term ?
Given sequence is, 1, 7, 13, 19, ....
Common difference (d) = 7-1=13-7=6
\(1^{st\\}\) term in the sequence (\(a_{1}\)) = 1
∴ \(a_{30}\) = \(a_{1}\) + (n-1)d
= 1+(30-1)×6
= 1+29×6
= 1+174
= 175
∴ 30th term is 175.
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