The first term of an arithmetic sequence is 5. the eleventh term is 125. what is the common difference of the arithemetic sequence?
(1,5);(11,125)
Rate of change=change in y/change in x
=125-5/11-1=120/10=12
☆☆☆☆☆common difference of the arithemetic sequence is 12
see the attached figure to better understand the problem
we have that

Step 1
<u>Find the value of AC</u>
we know that
in the right triangle ABC

substitute the values in the formula

Step 2
<u>Find the value of BC</u>
we know that
in the right triangle ABC
Applying the Pythagorean Theorem

substitute the values

Step 3
<u>Find the value of BD</u>
we know that
in the right triangle BCD
Applying the Pythagorean Theorem

substitute the values


therefore
<u>the answer is</u>
the length of BD is 11.93 units
We are given the equation:
<span>Z(q) = 4q + ½ --->
1</span>
The equation for z(u + 1/2) is obtained by
substituting q with u + ½ in the equation, therefore we can say that:
<span>q = u + ½ --->
2</span>
Substituting this value into equation # 1:
Z = 4 (u + ½) + ½ = z (u + 1/2)
4 u + 2 + ½ = z (u + 1/2)
<span>Since it was given that z (u +
1/2) = ½ then,</span>
4 u + 2 + ½ = ½
4 u + 2.5 = 0.5
4 u = -2
u = -1/2 (ANSWER)
<span> </span>