Math
posted by Crystal on .
I'm learning series and sequences (grade 11).
Please check that my steps show I understand what I'm doing/the concept and my answer as well:
5. The consecutive terms of an arithmetic sequences are 3.6, y, 8.2. Find the value of y.
This seems to be a sequence question but I used the formula for series.... Is there a better way to solve this question???
S3 = 3/2 (3.6+8.2)
=3/2(11.8)
=17.7
17.7 = 3/2(2 • 3.6 + (31)d)
17.7 = 3/2(7.2+2d)
17.7 = 10.8 + 3d
17.7  10.8 = 3d
6.9 = 3d
2.3 = d
So y = 5.9
I feel like I'm not doing this properly ... Please help! I have a quiz tomorrow on sequences ):
I also used the same method for this question:
Insert 3 evenly spaced numbers between 2 and 10. My final answer was 3 = d, so : 2, 1, 4, 7, 10.
What is the proper way to solve these questions? I don't think I'll be able to use series formulas on the quiz tomorrow which is only on sequences!
Also, I'm stuck on this question:
Find the 10th term of the arithmetic sequence where the first term is 5 and the 4th term is 17.
How would you solve this question?
Thank you so much in advance!

Consecutive numbers of an arithmetic have a common difference between them, that is ...
y  3.6 = 8.2y
2y = 11.8
y = 5.9
or
y must be "average" of the two other numbers
y = (3.6+8.2)/2 = 5.9
You sure went about it the long way.
For splacing 3 evenly spaced numbers between 2 and 10
2, , , , 10
then 2 must be the first term or a = 2
10 is th 5th term
term(5) = a + 4d
a+4d=10
2+4d=10
4d=12
d=3
Again, your answer is correct
last question:
given: fifth term is 5 > a+4d = 5
4th term is 17 > a+3d = 17
subtract the two equations
d = 12
then in a+3d = 17
a + 3(12) = 17
a= 17 + 36 = 53
term(10) = a+9d = 53 + 9(12) = 55
check:
if a=53, d = 12, the first few terms are
53 41 29 17 5 ...
our answer is correct 
Thank you so much Reiny!!

d doesnt = 12 because to subtract the 2 equations you would get 12d=18 then you whould have to devide and find that d=1.5