Question

How do you find the next three terms of the given arithmetic sequence 22, 20, 18, 16, …?

Answer 1

We start solving the problem by finding the first term of the given arithmetic sequence. We then find the common difference of the given arithmetic sequence by using the fact that the common difference of an arithmetic sequence is the difference of any two consecutive terms. We then find the required terms of the given arithmetic sequence by making use of the fact that the ${{n}^{th}}$ term in an arithmetic sequence is defined as ${{T}_{n}}=a+\left( n-1 \right)d$.

Complete step by step answer:
According to the problem, we are asked to find the next three terms of the given arithmetic sequence 22, 20, 18, 16, ….
We have given the arithmetic sequence 22, 20, 18, 16, ….
We can see that the first term of the given arithmetic sequence is $a=22$.
Now, let us find the common difference of the given arithmetic sequence. We know that the common difference of an arithmetic sequence is the difference of any two consecutive terms.
So, the common difference of the given arithmetic sequence is $d=20-22=-2$.
We have given the first four terms of the arithmetic sequence. We need to find the fifth, sixth and seventh term of that arithmetic sequence.
We know that the ${{n}^{th}}$ term in an arithmetic sequence is defined as ${{T}_{n}}=a+\left( n-1 \right)d$.
So, we have ${{T}_{5}}=a+4d=22+4\left( -2 \right)=14$.
$\Rightarrow {{T}_{6}}=a+5d=22+5\left( -2 \right)=12$.
$\Rightarrow {{T}_{7}}=a+6d=22+6\left( -2 \right)=10$.

$\therefore$ We have found the next three terms of the given arithmetic sequence as 14, 12, 10.

Note: Whenever we get this type of problems, we first try to find the first term and common difference of the given arithmetic sequence. We should not make calculation mistakes while solving this type of problem. We can also find the sum of the first 23 terms of the given arithmetic sequence. Similarly, we can expect problems to find the next three terms of the given sequence 1, 5, 25, 125, ….