Question

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 + (3-1)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!

Answer 1

Consecutive numbers of an arithmetic have a common difference between them, that is ...
y - 3.6 = 8.2-y
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

Answer 2

Thank you so much Reiny!!

Answer 3

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