In an arithmetic series t6 = −4, t10 = −12. find s10.

= - 30

Step-by-step explanation:

For a given arithmetic sequence the n th term formula is

= + (n - 1)d

where d is the common difference and the first term

We have to find d and

from the given information we can write 2 equations and solve for d and

= + 5d = - 4 → (1)

= + 9d = - 12 → (2)

subtract (1) from (2) term by term

4d = - 8 ⇒ d = - 2

substitute d = - 2 in (1)

- 10 = - 4 ⇒ = - 4 + 10 = 6

The sum to n terms of an arithmetic sequence is

= [2 + (n - 1)d ], hence

= 5[(2 × 6) + (9 × - 2) ] = 5(12 - 18) = 5 × - 6 = - 30

the distance from any point on the parabola to the focus is the exact same as the distance from that point to the directrix.

if you could provide answer choices that might allow me to answer the question easier if my above answer isn't an option! (: