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

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt