Question

Which expression defines the given series for seven terms? -13 + (-16) + (-19) +...

Answer 1

`- 13 + ( - 3) = - 16 \\ - 16 + ( - 3) = - 19 \\ - 19 + ( - 3) = - 22 \\ - 22 + ( - 3) = - 25`
you have to plus (-3) for each numbers

Answer 2

`a_n =-3n-10`

Explanation:

-13 + (-16) + (-19) +...

Difference between two terms = -3

-16 -(-13)= -3

-19 -(-16)= -3

Common difference is a constant so it is arithmatic

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

where 'd' is the difference = -3

a1 is the first term that is -13

`a_n = -13+(n-1)(-3)`

`a_n = -13-3n+3`

Combine like terms

`a_n =-3n-10`