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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Which of the following represents the general term for the sequence 1, 3, 5, 7, 9, . . .?
2n - 1, n, n + 2, 2n
Solution:
It is given that
The sequence that is given to us is 1, 3, 5, 7, 9, ...
Let us assume a1 = 1, a2 = 3, a3 = 5, a4 = 7, a5 = 9
Then,
a2 - a1 = 3 - 1 = 2
a3 - a2 = 5 - 3 = 2
a4 - a3 = 7 - 5 = 2
a5 - a4 = 9 - 7 = 2.
Hence, from the above simplification we can see that the common difference is 2.
So, the nth term of an arithmetic progression whose first term a1 = 1 and common difference d = 2 is given by,
an = a1 + (n - 1) d
Substituting the values:
an = 1 + (n - 1) 2
= 1 + 2n - 2
= 2n - 1
Therefore, the general term for the sequence 1, 3, 5, 7, 9, . . . is 2n - 1.
Which of the following represents the general term for the sequence 1, 3, 5, 7, 9, . . .?
2n - 1, n, n + 2, 2n
Summary:
The general term for the sequence 1, 3, 5, 7, 9, . . . is 2n - 1.
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