Question

Find the \[{10^{th}}\] term of the pattern whose terms are given by rule.
\[\left( a \right){\text{ }}n - 1\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left( b \right){\text{ }}2n + 3\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left( c \right){\text{ }}{n^2} - 1\]

Answer 1

Hint: Put given value of in the nth term formula of the given pattern to get the asked or respective term of the pattern.

Complete step by step answer:
A.(1) Given pattern of nth term is written as \[{T_n} = (n - 1)\]
Where represents the nth term of the series or pattern.
(2) For calculating 10th term, we use \[n = 10\] in formula mentioned in step \[\left( 1 \right)\]
\[{T_{10}} = (10 - 1)\]
\[\therefore \,\,{T_{10}} = 9\]
Hence, the 10th term of the pattern whose term is given as \[\left( {n - 1} \right)\] is $9$.

B.(1) Given pattern of nth term of the pattern is written as
\[{T_n} = (2n + 3)\] where ‘n’ is the nth term of the pattern.
(2) For calculating the 10th term we use \[n = 10\] in the above mentioned formula.
\[{T_{10}} = 2(10) + 3\]
\[ = 20 + 3\]
\[{T_{10}} = 23\]
Hence, 10th term of the pattern whose terms are given by \[\left( {2n + 3} \right){\text{ }}is{\text{ }}23.\]

C. (1) Given pattern of nth term is written as\[{T_n} = {n^2} - 1\]
Where ‘n’ is the nth term of the pattern.
(2) For calculating 10th term we use \[n = 10\] in above mentioned formula
\[{T_{10}} = {(10)^2} - 1\]
\[ = 100 - 1\]
\[ = 99\]
Hence, 10th term of the pattern whose term is given by \[\left( {{n^2} - 1} \right){\text{ }}is{\text{ }}99.\]

Additional Information: A pattern is a series of sequences that repeats. There are two main types of math patterns, number patterns or sequence of numbers arranged according to a rule or rules and shape patterns, which are labelled by using letters and the way that they repeat.
For example: \[{T_{10}} = 99\]


Note: nth term is also known as the general term of the pattern. It helps to calculate any particular term of the pattern without writing the actual pattern.