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6. In the sequence [tex]\(1, 2, 3, 4, 5, \ldots\)[/tex], the value of any term in the sequence equals [tex]\(n\)[/tex], the number of the term itself. Write an expression, in terms of [tex]\(n\)[/tex], that will give the value of any term in the sequence [tex]\(1, 4, 9, 16, 25, \ldots\)[/tex].



Answer :

GinnyAnswer
To find the value of any term in the sequence 1, 4, 9, 16, 25, we first need to identify the pattern in the sequence. Let's examine the given terms:

1st term: 1
2nd term: 4
3rd term: 9
4th term: 16
5th term: 25

We can see that these terms are perfect squares:
1 = 1²
4 = 2²
9 = 3²
16 = 4²
25 = 5²

From these observations, we can conclude that the value of the nth term in this sequence corresponds to the square of n.

So, if we denote the nth term of the sequence by [tex]\(a_n\)[/tex], we have:
[tex]\[a_n = n^2\][/tex]

Therefore, the expression that gives the value of the nth term in the sequence 1, 4, 9, 16, 25 is:
[tex]\[a_n = n^2\][/tex]

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