In Geometric Series How do you figure out what n would be? 3+6+12+...+192?

Answer 1

You haven't stated what n is in this situation. n usually represents the power to which the common ratio has been raised, in which case you need to calculate the common ratio first. You can see that each element is twice the element before, because 12/6 = 6/3 = 2, so the common ratio is 2. The last number, 192, is 3*64 = 3*2^6, so n = 6.

But if n is the sum of the geometric series, usually written as S (but I have no way to know what you intended), the formula is a*(1 - r^(n+1))/(1 - r), where a is the first element in the series, r is the common ratio, and n is the index number of the last term (where the first term has an index of 0), or the power to which the common ratio has been raised in the last term. You can see that 12/6 = 6/3 = 2, the common ratio. The first term is 3. 192 = 3*64 = 3*2^6, so n = 6. Then S = 3*(1 - 2^(6+1))/(1 - 2) = 3*(1 - 2^7)/(-1) = -3*(1 - 128) = 3*127 = 381.

Answer 2

You have to find what the relationship to each term is, and it is usually done by inspection. In this case, after 3, each term is twice the previous term, so the sequence would be:
3+6+12+24+48+96+192, or
3*(2**0+2**1+2**2+2**3+2**4+2**5+2**6). Sum the terms = 381 = 3*127 = 3 * (2**7-1). Formula then = base number (3) X (2**(n+1)), where, in my example, n is the largest exponent.)

I assume "n" in your question is the sum of all numbers, not the base of the power series - your question does not specify.)

Answer 3

In Geometric Series How do you figure out what n would be? 3+6+12+...+192?
The common multiplier is 2. The nth term is 3*2^(n-1).

If you are asking what the value of n is for 192, then
3*2^(n-1)=192
2^n-1 = 64
2^(n-1) = 2^6
n-1 =6
n=7
then 192 is the 7th term in the given sequence.

Answer 4

an = a1 * r^(n - 1)

an = 3 * 2^(n - 1)
192 = 3 * 2^(n - 1)
64 = 2^(n - 1)
2^6 = 2^(n - 1)
6 = n - 1
n = 7

Sn = (a1 * (1 - r^n))/(1 - r)

S(7) = (3(1 - 2^7))/(1 - 2)
S(7) = (3(1 - 128))/(-1)
S(7) = -3(-127)
S(7) = 381

ANS : 3 + 6 + 12 + ... + 192 = 381

Answer 5

a=3
r=2
tn=192
n=?

tn=ar^n-1
192=(3)2^n-1
64=2^n-1
Now, at this point if you have the same base on either side, the exponent will be equal.
2^6=2^n-1
6=n-1
7=n
Therefore, there are 7 terms in the sequence.