Question

What is the next number in the sequence 82, 101, 122, 145?

Answer 1

Hint: For solving this question you should know about the sequence & arithmetic sequence. In the arithmetic sequence we can find a term like arithmetic progression. We have to only find the first term and the sequence between two continuous terms and the term’s place which we have to find. But in a sequence we always find the difference between two terms. According to the question we have to find the next number in the sequence 82, 101, 122, 145.

Complete step by step answer:
For calculating the next number we have to find the difference between two successive terms.
For calculating the next or last digits we always determined the difference between the successive or continuous. Because this will give an induction for making our next digit as successive as all digits of sequence are present.
So the difference between two successive terms is as follows: -
\[\begin{align}
  & 101-82=19 \\
 & 122-101=21 \\
 & 145-122=23 \\
\end{align}\]
So, the final terms are 19, 21 and 23 and all these have a difference of 2. These are constantly increasing by 2, next term will be \[23+2=25\].
So, if the next increased term is 25, then if we calculate the next term, then we add the next digit in the last digit for getting the next digit’s original value.
So, by adding 25 in last digit of a sequence:
\[145+25=170\]

Hence, the next digit of sequence 82, 101, 122, 145 will be 170.

Note: The arithmetic sequence is only used if we are calculating any term for a sequence. It is not used in the calculation of Arithmetic progression (A.P.). Because both are different terms so they can not be calculated by the same formula. It is always in a fixed sequence and always in fixed values.