Question

Which of the following equations could be used to solve for the tenth term of the following sequence?

15, 13, 11, 9, ...


A(10) = 15 + 10(-2)
A(10) = 15 + 9(-2)
A(10) = 15 + 9(2)
A(10) = 15 + 10(2)

Answer 1

the formula would be : an = a1 + (n - 1) * d
where n is the term u want to find, which is 10.......a1 = first term = 15...d is common difference = -2.
A(10) = 15 + (10 - 1) * -2.....
A(10) = 15 + 9(-2) <===

Answer 2

Option(B) is correct.

The tenth term is given by
`a_(10)=15+9(-2)`

Explanation:

Given : The sequence 15, 13, 11, 9,....

We have to determine the equation that can be used to find the tenth term of the given sequence 15, 13, 11, 9,....

Consider the given sequence 15, 13, 11, 9,..

`a_1= 15, a_2=13, a_3= 11`

Difference between each term is

`a_2-a_1=13-15=-2\\ a_3-a_2=11-13=-2`

Since, The difference between each term is constant -2

Thus, The given sequence is an arithmetic sequence with first term 15 and common difference -2.

Thus, The general term is given by

`a_n=a+(n-1)d`

where a is first term and d is common difference nd n is number of term.

Subsitute, we have,

`a_(10)=15+(10-1)(-2)`

Simplify, we have,

`a_(10)=15+9(-2)`

Thus, The tenth term is given by
`a_(10)=15+9(-2)`