Question

Find the term \[{{t}_{10}}\] of an \[A.P.4.9.14,.....?\]

Answer 1

Hint: This question is from arithmetic progression which is series. In the A.P. series simply put the formula and solve it. Where n = term number, d = difference between the two terms, a = first term, term value.
\[{{t}_{n}}=a+\left( n-1 \right)d\]

Complete step-by-step answer:
In the series given a (first term) \[=4\]
Number of term is given \[\left( n \right)=10\]
\[d={{a}_{2}}-{{a}_{1}}\]
\[d=9-4=5\]
By putting these values in equation:
\[{{t}_{10}}=4+\left( 10-1 \right)\times 5\]
\[{{t}_{10}}=4+9\times 5\]
\[{{t}_{10}}=4+45\]
\[{{t}_{10}}=49\]
So the value of \[{{t}_{10}}\] is 49.

Note: Firstly, write given values and then write what we have to find, then put all the values in formula. From the given sequence, we can easily read off the first term and common difference
d = regular contrast of any pair of back to back or contiguous numbers
There are three things needed to examine for calculating the nth term by using the formula.
the first term (a1​)
the common difference between consecutive terms (d)
and the term position (n)