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Yuki888 [10]
3 years ago
14

What is the nth term in the sequence: 4, 7, 12, 19, 28 Please show working out

Mathematics
2 answers:
Fynjy0 [20]3 years ago
4 0

Answer:

The nth term in the given sequence will be:

n^2+3

Step-by-step explanation:

We are given a sequence as:

4,7,12,19,28,....

Let a_n represents the nth term in the sequence.

i.e. a_1=4\\\\a_2=7\\\\a_3=12\\\\a_4=19\\\\a_5=28

i.e. these terms could also be written as:

a_1=(1)^2+3\\\\a_2=(2)^2+3=7\\\\a_3=(3)^2+3=12\\\\a_4=(4)^2+3=19\\\\a_5=(5)^2+3=28\\\\.\\.\\.\\.\\.\\.\\.a_n=(n)^2+3=n^2+3

Hence the nth term in the given sequence will be:

n^2+3

Anna71 [15]3 years ago
3 0
<span>The correct answer is n</span>²<span>+3.

Explanation<span>:
We find the first differences between terms:
7-4=3; 12-7=5; 19-12=7; 28-19=9.

Since these are different, this is not linear.

We now find the second differences:
5-3=2; 7-5=2; 9-7=2.

Since these are the same, this sequence is quadratic.
We use (1/2a)n</span></span>²<span><span>, where a is the second difference:
(1/2*2)n</span></span>²<span><span>=1n</span></span>²<span><span>.

We now use the term number of each term for n:
4 is the 1st term; 1*1</span></span>²<span><span>=1.
7 is the 2nd term; 1*2</span></span>²<span><span>=4.
12 is the 3rd term; 1*3</span></span>²<span><span>=9.
19 is the 4th term; 1*4</span></span>²<span><span>=16.
28 is the 5th term: 1*5</span></span>²<span><span>=25.

Now we find the difference between the actual terms of the sequence and the numbers we just found:

4-1=3; 7-4=3; 12-9=3; 19-16=3; 28-25=3.

Since this is constant, the sequence is in the form (1/2a)n</span></span>²<span><span>+d;
in our case, 1n</span></span>²<span><span>+d, and since d=3, 1n</span></span>²<span><span>+3.</span></span>
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