Question

Someone please help I dont understand

Answer 1

The series -13, -7, -1, 5, 11 follows a pattern of adding 6 to each term successively. The representation that fits this progression is: -13 + 6K, where K denotes the term's position.

The given series is:

-13 + (-7) + (-1) + 5 + 11

This series forms a sequence by adding 6 to each consecutive term.

To represent this sequence in terms of an equation or expression, we can use a general formula:

`\[ a_n = a_1 + (n - 1) \cdot d \]`

Where:

`\(a_n\)` represents the nth term in the sequence.

`\(a_1\)` is the first term.

`\(n\)` is the term number.

`\(d\)` is the common difference between terms.

For this series, the first term
`(\(a_1\))` is -13, and the common difference
`(\(d\))`is 6.

Let's find the 5th term in the sequence (as given series contains 5 terms):

`\[ a_5 = a_1 + (5 - 1) \cdot d \]`

`\[ a_5 = -13 + 4 \cdot 6 \]`

`\[ a_5 = -13 + 24 \]`

`\[ a_5 = 11 \]`

The 5th term of the sequence is indeed 11, confirming that the pattern of adding 6 to each consecutive term holds true. Therefore, the correct representation corresponding to this series is: -13 + 6K, where
`\(K\)`represents the position of the term in the sequence.

Answer 2

The answer is
`\sum_(k=1)^(5)-13+6k` . The last option is correct.

This is because we can see from the image that the series is arithmetic with a common difference of 6. The first term of the series is −13 and there are 5 terms in the series.

Therefore, the sum of the series is given by
`\sum_(k=1)^(5)-13+6k`

We can also see from the image that the series is equal to the sum of the following two series:

= -13+(-7)+(-1)+5+11 &= -13+(-7)+(-1)+(5+11)

`= -13+(-7)+(-1)+16`

`= \sum_(k=1)^(3)-13+6k`

and

= -13+(-7)+(-1)+5+11

= (-13+5)+(11-7)+(-1)

= -8+4+(-1)

= -5

`= \sum_(k=1)^(1)-19+6k`

Therefore, the sum of the series is given by

`-13+(-7)+(-1)+5+11 &= \sum_(k=1)^(3)-13+6k + \sum_(k=1)^(1)-19+6k`

`= \sum_(k=1)^(5)-13+6k`

Last option is correct.