SOLUTION: THE 2ND AND 7TH TERM OF A G.P ARE 18 AND 4374 RESPECTIVELY. FIND THE 1) COMMON DIFFERENCE 2) FIRST TERM 3) SUM OF THE 4TH AND 8TH TERM 4) SUM OF THE FIRST 10 TERMS

Algebra ->  Sequences-and-series -> SOLUTION: THE 2ND AND 7TH TERM OF A G.P ARE 18 AND 4374 RESPECTIVELY. FIND THE 1) COMMON DIFFERENCE 2) FIRST TERM 3) SUM OF THE 4TH AND 8TH TERM 4) SUM OF THE FIRST 10 TERMS      Log On


   

Question 1210345: THE 2ND AND 7TH TERM OF A G.P ARE 18 AND 4374 RESPECTIVELY. FIND THE
1) COMMON DIFFERENCE
2) FIRST TERM
3) SUM OF THE 4TH AND 8TH TERM
4) SUM OF THE FIRST 10 TERMS
Found 5 solutions by josgarithmetic, Edwin McCravy, mccravyedwin, ikleyn, AnlytcPhil:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
What kind of pattern is this? "A G P ARE..."?
Geometric Progression? Why you ask for "COMMON DIFFERENCE"?

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
I'll assume the student meant

THE 2ND AND 7TH TERM OF A G.P ARE 18 AND 4374 RESPECTIVELY. FIND THE 
1) COMMON RATIO 
2) FIRST TERM 
3) SUM OF THE 4TH AND 8TH TERM
4) SUM OF THE FIRST 10 TERMS

1) COMMON RATIO 


a%5B1%5D=a%2Ar%5E%282-1%29=ar=18
a%5B7%5D=a%2Ar%5E%287-1%29=ar%5E6=4374

Divide the second equation term-by-term by the first equation.

%28a%5B6%5Dr%5E6%29%2F%28a%5B1%5Dr%29=4374%2F18

r%5E5=243

r+=+root%285%2C243%29

r+=+3

2) FIRST TERM 

a%5B1%5Dr=18
a%5B1%5D%2A3=18
a%5B1%5D=18%2F3
a%5B1%5D=6

3) SUM OF THE 4TH AND 8TH TERM

Using a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29

a%5B4%5D=a%5B1%5D%2Ar%5E%284-1%29=6%2A3%5E3=6%2A27=162

a%5B8%5D=a%5B1%5D%2Ar%5E%288-1%29=6%2A3%5E7=6%2A2187=13122 

a%5B4%5D%2Ba%5B8%5D=+162%2B13122=13284

4) SUM OF THE FIRST 10 TERMS

S%5Bn%5D=a%5B1%5D%2Aexpr%28%28r%5En-1%29%2F%28r-1%29%29%29



Edwin

Answer by mccravyedwin(406) About Me  (Show Source):
You can put this solution on YOUR website!
Now I'll assume the student meant

THE 2ND AND 7TH TERM OF AN A.P ARE 18 AND 4374 RESPECTIVELY. FIND THE 
1) COMMON DIFFERENCE 
2) FIRST TERM 
3) SUM OF THE 4TH AND 8TH TERM
4) SUM OF THE FIRST 10 TERMS

I'll use a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

1) COMMON DIFFERENCE 


a%5B2%5D=a%5B1%5D%2B%282-1%29d=a%5B1%5D%2Bd=18
a%5B7%5D=a%5B1%5D%2B%287-1%29d=a%5B1%5D%2B%287-1%29d=a%5B1%5D%2B6d=4374

Subtract the first equation term-by-term from the second equation.

%28a%5B1%5D%2B6d%29-%28a%5B1%5D%2Bd%29=4374-18

5d=4356

d+=+4356%2F5%29

d+=+871.2

2) FIRST TERM 

a%2Bd=18

a%5B1%5D%2B871.2=18
a%5B1%5D=18-871.2
a%5B1%5D=-853.2

3) SUM OF THE 4TH AND 8TH TERM

Using a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

a%5B4%5D=a%5B1%5D%2B%284-1%29%2A871.2=-853.2%2B3%2A871.2=-853.2%2B2613.6=1760.4

a%5B8%5D=a%5B1%5D%2B%288-1%29%2A871.2=-853.2%2B7%2A871.2=-853.2+%2B+6098.4=5245.2 

a%5B4%5D%2Ba%5B8%5D=+1760.4%2B5245.2=7005.6

4) SUM OF THE FIRST 10 TERMS

S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29



S%5B10%5D=5%28-1706.4%2B7840.8%29%29

S%5B10%5D=5%286134.4%29=30672

Edwin

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

To avoid misunderstanding, here is my correction to the post by Edwin,
where he placed his solution for Geometric progression.


His last formula in his post should be

S%5B10%5D = 6%2A%28%283%5E10-1%29%2F%283-1%29%29 = 6%2A%2859048%2F2%29 = 6*29524 = 177144.


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As  I  see from the  Edwin's post  (as  @AnlytcPhil),  Edwin did not get the meaning of my correction.

The meaning is not in placing parentheses.

The meaning is that  I  changed  ' 10-1 '  in the denominator by  ' 3-1 ',
and then changed  ' 9 '  in the denominator by  ' 2 '  to make the numbers consistent.



Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!

Ikleyn says:

To avoid misunderstanding, here is my correction to the post by Edwin, 
where he placed his solution for Geometric progression.
His last formula in his post should be


S%5B10%5D = 6%2A%28%283%5E10-1%29%2F%283-1%29%29 = 6%2A%2859048%2F2%29 = 6*29524 = 177144.

And if you'll notice, that's exactly what I had



Parentheses are not necessary.

Edwin