Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# Write the first three terms in each of the sequence defined by the following:1) ${a_n} = 3n + 2$2) ${a_n} = {n^2} + 1$

Last updated date: 13th Jun 2024
Total views: 413.1k
Views today: 8.13k
Verified
413.1k+ views
Hint: The sequence of each term gives as many different values.
Our discussion for this sequence is about the first three terms only. Yet the sequence ${a_n}$ has n number of values, when we put different values to the sequence it gives a different number.
Now, we are going to substitute positive integers for n of order $1,2,3$ that is ${a_1},{a_2},{a_3}$.

1) ${a_n} = 3n + 2$
Take n values for first three terms
So, $n = 1,2,3$ we get
If we take $n = 1$ ,
$\Rightarrow {a_1} = 3(1) + 2$
$\Rightarrow {a_1} = 3 + 2$
$\Rightarrow {a_1} = 5$
If we take $n = 2$ ,
$\Rightarrow {a_2} = 3(2) + 2$
$\Rightarrow {a_2} = 6 + 2$
$\Rightarrow {a_2} = 8$
If we take $n = 3$ ,
$\Rightarrow {a_3} = 3(3) + 2$
$\Rightarrow {a_3} = 9 + 2$
$\Rightarrow {a_3} = 11$
Hence we get, ${a_1} = 5,{a_2} = 8,{a_3} = 11$
The first three terms for the sequence ${a_n} = 3n + 2$ is $5,8,11$

2) ${a_n} = {n^2} + 1$
Take n values for first three terms
So, $n = 1,2,3$
If we take $n = 1$
$\Rightarrow {a_1} = {1^2} + 1$
$\Rightarrow {a_1} = 1 + 1$
$\Rightarrow {a_1} = 2$
If we take $n = 2$ ,
$\Rightarrow {a_2} = {2^2} + 1$
$\Rightarrow {a_2} = 4 + 1$
$\Rightarrow {a_2} = 5$
If we take $n = 3$ ,
$\Rightarrow {a_3} = {3^2} + 1$
$\Rightarrow {a_3} = 9 + 1$
$\Rightarrow {a_3} = 10$
Hence we get, ${a_1} = 2,{a_2} = 5,{a_3} = 10$
$\therefore$The first three terms for the sequence ${a_n} = {n^2} + 1$ is $2,5,10$

Note:Form the above observation in first sequence ${a_n} = 3n + 2$
if n is an odd number, the sequence is odd.
If n is an even number, the sequence is even.
In same way, the sequence ${a_n} = {n^2} + 1$
If n is an odd number, the sequence is even.
If n is an even number, the sequence is odd.
Both the sequences have n number of terms, for our convenience we take the first three terms. In some cases, they ask randomly, give value for $n = 10$ or $n = 20$ for the sequence, we can find that also by substitution.