The sum of the given sequence is -6384.
<u>Step-by-step explanation:</u>
The given Arithmetic sequence is 14 + 8 + 2+ ... + ( 274) + (-280).
- The first term of the sequence = 14
- The last term of the sequence = -280
- The common difference ⇒ 14 - 8 = 6
<u>To find the number of terms in the sequence :</u>
The formula used is
where,
- n is the number of terms.
- is the late term which is -280.
- is the first term which is 14.
- d is the common difference which is 6.
Therefore,
⇒
⇒
⇒
⇒ n = 48, since n cannot be negative.
∴ The number of terms, n = 48.
<u>To find the sum of the arithmetic progression :</u>
The formula used is
where,
- S is the sum of the sequence.
- is the first term which is 14.
- is the late term which is -280.
Therefore,
⇒
⇒
⇒
∴ The sum of the given sequence is -6384.
Width of the box is 9 inches
Step-by-step explanation:
- Step 1: Calculate width of the box when volume, V = 486 in³, length, l = 18 in and height, h = 3 in
Formula for width of the box, w = V/l × h
⇒ w = 486/18 × 3
= 486/54 = 9 in
Just scan it, there’s an answer for it already I’m pretty sure
Answer:
4
Step-by-step explanation:
When M varies inversely P squared rhen this is represented as
Here, k is a constant of proportionality
Now when M is 9 and P is 2, P squared will be 4. Now substituting the value of P squared and M into the equation we can find the xonstant of proportionality as
K=9*4=36
Now that we have k, when P is 3 then we substitute the value of P as 3 and k as 36 into the first equation hence
Therefore, M=4