Question

Find the first three terms of the sequence below. T n = n 2 + 4 n + 2

Answer 1

Answer:

Step-by-step explanation:

The given sequence is T  

n

​  

=n  

2

+4 where T  

n

​  

=200.

Substitute T  

n

​  

=200 in the sequence T  

n

​  

=n  

2

+4 as follows:

T  

n

​  

=n  

2

+4

⇒200=n  

2

+4

⇒n  

2

=200−4=196

⇒n  

2

=196

⇒n=  

196

​  

=14

Hence, n=14

Answer 2

Given,

$\[{T_n} = {n^2} + 4n + 2\]$

Solution,

Calculate the first three terms of the sequence.

$\[\begin{array}{l}n = 1\\{T_n} = {n^2} + 4n + 2\\ \Rightarrow {T_1} = {1^2} + 4 \times 1 + 2\\ \Rightarrow {T_1} = 1 + 4 + 2\\ \Rightarrow {T_1} = 7\\n = 2\\{T_n} = {n^2} + 4n + 2\\ \Rightarrow {T_2} = {2^2} + 4 \times 2 + 2\\ \Rightarrow {T_2} = 4 + 8 + 2\\ \Rightarrow {T_2} = 14\\n = 3\\{T_n} = {n^2} + 4n + 2\\ \Rightarrow {T_3} = {3^2} + 4 \times 3 + 2\\ \Rightarrow {T_3} = 9 + 12 + 2\\ \Rightarrow {T_3} = 23\end{array}\]$

Hence the first three terms of sequence is $\[7,14,23\]$