Question

5th term of sequence define as a1 =a2=3,a3=a1+a2,an=2an-1+3n>=4
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Answer 1

Step-by-step explanation:

hope it is helpful for seen the answer

Answer 2

Given:

$\[{a_1} = {a_2} = 3\]$, $\[{a_3} = {a_1} + {a_2}\]$ And $\[{a_n} = 2{a_{n - 1}} + 3\]$

Solution:

To find $\[{5^{th}}\]$ term $\[{a_5}\]$, first find $\[{a_4}\]$ using $\[{a_n} = 2{a_{n - 1}} + 3\]$,

$\[\begin{array}{l}{a_4} = {a_{4 - 1}} + 3\\ \Rightarrow {a_4} = {a_3} + 3\end{array}\]$

Put, $\[{a_3} = {a_1} + {a_2}\]$ and $\[{a_1} + {a_2} = 3 + 3\]$,

$\[\begin{array}{l}{a_4} = 3 + 3 + 3\\{a_4} = 9\end{array}\]$

Now find $\[{a_5}\]$,

$\[\begin{array}{l}{a_5} = {a_{5 - 1}} + 3\\ \Rightarrow {a_5} = {a_4} + 3\\ \Rightarrow {a_5} = 9 + 3\\ \Rightarrow {a_5} = 12\end{array}\]$

Hence, 5th term of sequence is 12.