Answer:
a) n2+ 3
So, first term is (1)²+3=4
Second term is (2)²+3=7
Third term is (3)²+3=12
Fouth term is (4)²+4=20
b) 2n2
So, first term is (1)²+2=3
Second term is (2)²+2=6
Third term is (3)²+2=11
Fouth term is (4)²+2=18
Answer:
( a )
First 4 terms are 4,7,12,19 and the 10th term is 103.
( b )
First 4 terms are 2,8,18,32 and the 10th term is 200.
Step-by-step explanation:
We are given both general term of sequence:
[tex] \displaystyle \large{ (a) \: \: \: {n}^{2} + 3} \\ \displaystyle \large{ (b) \: \: \: 2{n}^{2}}[/tex]
Let's get to the first sequence.
( a )
We are given:-
[tex] \displaystyle \large{ {n}^{2} + 3} [/tex]
To find first 4 terms, substitute n = 1,2,3,4 in.
Therefore:-
[tex] \displaystyle \large{ {1}^{2} + 3 = 4} \\ \displaystyle \large{ {2}^{2} + 3 = 4 + 3 = 7} \\ \displaystyle \large{ {3}^{2} + 3 = 9 + 3 = 12} \\ \displaystyle \large{ {4}^{2} + 3 = 16 + 3 = 19} [/tex]
Therefore, first 4 terms are 4,7,12,19.
Next, to find the 10th term, just substitute n = 10.
[tex] \displaystyle \large{ {10}^{2} + 3 = 100 + 3 = 103} [/tex]
And we're done for part a!
( b )
We are given:-
[tex] \displaystyle \large{ 2{n}^{2}}[/tex]
Do the same, substitute n = 1,2,3,4 in.
[tex] \displaystyle \large{ 2({1})^{2} = 2} \\ \displaystyle \large{ 2({2})^{2} = 2(4) = 8} \\ \displaystyle \large{ 2({3})^{2} = 2(9) = 18} \\ \displaystyle \large{ 2({4})^{2} = 2(16) = 32}[/tex]
Therefore, first 4 terms are 2,8,18,32.
Next, find the 10th term, substitute n = 10 in.
[tex] \displaystyle \large{ 2{(10)}^{2} = 2(100) = 200} [/tex]
Thus, the 10th term is 200.
