Question

Using your formula for the sequence in the second arithmetic problem from above (-10, -5, 0, 5, ...), find a₁₅.

Answer 1

The value of
`\(a_(15)\)` in the sequence (-10, -5, 0, 5, ...) is 70.

Step-by-step explanation:

In an arithmetic sequence, each term is determined by adding a common difference to the previous term. In this case, the common difference is 5 because each term increases by 5. To find
`\(a_(15)\)`, we use the formula
`\(a_n = a_1 + (n-1)d\),` where
`\(a_n\)`is the nth term,
`\(a_1\)` is the first term, (n) is the number of terms, and (d) is the common difference.

First, identify the values:

-
`\(a_1\)` (the first term) is -10,

- (n) (the number of terms) is 15,

- (d) (the common difference) is 5.

Now, substitute these values into the formula:

`\[ a_(15) = -10 + (15-1) * 5 \]`

Simplify the expression:

`\[ a_(15) = -10 + 14 * 5 \]`

[ a_{15} = -10 + 70 ]

[ a_{15} = 60 ]

So, (a_{15}) is 70 in the given sequence.

In conclusion, by applying the formula for arithmetic sequences, we determined that the 15th term in the sequence (-10, -5, 0, 5, ...) is 70. The common difference of 5 and the initial term of -10 were used to calculate this value through the arithmetic sequence formula.