Geometric Sequences

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raybies

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The sum of the first 10 terms of a geometric sequence is 4−2−8. If the common ratio is 1/2, find the first term of the sequence. Use this to determine the 11th term of the sequence.
 
So a + a(1/2) + a(1/2)^2 + ... + a(1/2)^9 = 4-2^(-8)
Solve this for a.

11th term is a(1/2)^10
 
Jomo said:
So a + a(1/2) + a(1/2)^2 + ... + a(1/2)^9 = 4-2^(-8)
Solve this for a.

11th term is a(1/2)^10
Click to expand...

So, you solve a(1/2)^2, assuming that the other side is 0, you get 0. Is this an error or is this intended? Thank you for your help however!
 
raybies said:
So, you solve a(1/2)^2, assuming that the other side is 0, you get 0. Is this an error or is this intended? Thank you for your help however!
Click to expand...
a(1/2)^2 is not an equation, there is no equal sign. You can't assume "the other side" if it's not given.
The equation is
a + a(1/2) + a(1/2)^2 + ... + a(1/2)^9 = 4-2^(-8)
And a is the unknown. Solve it. Then plug in the value of a into the expression for the 11th term.
To solve the equation you may want to simplify it first - look up the formula for the sum of a geometric sequence.
 
a + a(1/2) + a(1/2)^2 + ... + a(1/2)^9 = a((1/2)^0 + (1/2)^1 + (1/2)^2 + ... + (1/2)^9) = 4-2^(-8). Solve for a. Does division come to mind?
 
Last edited:
raybies said:
The sum of the first 10 terms of a geometric sequence is 4−2−8. If the common ratio is 1/2, find the first term of the sequence. Use this to determine the 11th term of the sequence.
Click to expand...
Do a google search with key-words:

sum of geometric series.​

If you are still confused, come beck and tell us what you found and what you don't understand.
 
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