Question

Calculate the arithmetic sequence in which a9=17 and the common difference is d=-2.1

Answer 1

The correct answer is d-71.3

Explanation:

Answer 2

`S_(31)=71.3`

Explanation:

The nth term of an arithmetic sequence is given by the formula,

`U_n=a_1+(n-1)d`

We were given that the 9th term is
`17`.

`\Rightarrow 17=a_1+(9-1)(-2.1)`

`\Rightarrow 17=a_1+(8)*(-2.1)`

`\Rightarrow 17=a_1-(84)/(5)`

`\Rightarrow 17+(84)/(5)=a_1`

`\Rightarrow a_1=(169)/(5)`

The sum of the first n-terms is given by the formula,

`S_n=(n)/(2)(2a_1+(n-1)d)`

To find
`S_(31)`, we substitute
`n=31`,
`a_1=(169)/(5)` and
`d=-2.1`.

`\Rightarrow S_(31)=(31)/(2)(2((169)/(5)+(31-1)(-2.1))`

`\Rightarrow S_(31)=(31)/(2)(2((169)/(5)+(30)(-2.1))`

`\Rightarrow S_(31)=(31)/(2)((23)/(5))`

`\Rightarrow S_(31)=(713)/(10)`

`\Rightarrow S_(31)=71.3`

The correct answer is D