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C2 GP

Find the number of terms in each of these geometric progressions

3,6,12,...,768 well i just want to know how to do this then ill know all of em

Reply 1

Killjoy-

The general form of any term in a GP is

ab^{r-1}

, r is the term-to-term ratio, 2 in this case, and a must be 3.

So set 768 to the equation for the general form and solve for n. (n is the term number of the last term in the sequence.)

(edited 11 years ago)

Reply 2

Ganhad

did that its not happening :biggrin:

dont know how to get past that

Reply 3

Killjoy-

768=3 \times 2^{n-1}

You'll need to take logs to base 2. (Or any base for that matter but 2 is simpler.)

n-1=log_2(256)

Reply 4

raheem94

Original post by Ganhad

did that its not happening :biggrin:

dont know how to get past that

768=3 \times 2^{n-1}

Divide both sides by 3,

256 = 2^{n-1} \implies 256 = 2^n \times 2^{-1} \implies 256 = 2^n \times \frac12 \implies 512 = 2^n

Now take logs.

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