Question

The arithmetic sequence 1, 3, 5, 7, 9,. . . Represents the set of odd natural numbers. What is the explicit rule for the sequence? ak = (k - 1).

Answer 1

The explicit rule for the sequence is Tn = 2n - 1

Given the sequence 1, 3, 5, 7, 9...

The explicit formula for the nth term is expressed as:

$T_n=a+(n-1)d$

a is the first term = 1

d is the common difference = 3 - 1 = 5 - 3 = 2

n is the number of terms

Substitute the given parameters into the formula to have;

$T_n = 1+(n-1)(2)\\T_n=1+2n-2\\T_n=2n-1$

Hence the explicit rule for the sequence is Tn = 2n - 1

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Answer 2

Answer:

1st: 1+(k-1)2

2nd: 399

3rd: C

4th: 40,000