The second term of a geometric sequence is 9 and the fourth term is 81. Find the sum of the first 10 terms of this sequence.
How can I find the answer?
I need help with this one too
Find the Sum the 4 terms
10, 30, 90, 270, ...
r=3
nth term= 3^n
sn= sum from n=1 to 10
Sn= 3+3^2 + 3^3 + ...+3^10
http://www.dummies.com/education/math/calculus/how-to-find-the-partial-sum-of-a-geometric-sequence/
On the second, you have the four terms, add them.
I dont understand
You must know the basic formulas for a geometric sequence.
term(n) = a r^(n-1), where a is the first term, r is the common ratio and n is the term number
for yours:
ar = 9 and ar^3 = 81
divide one equation by the other:
ar^3/(ar) = 81/9
r^2 = 9
r = ± 3
then ar = 9
So if r = 3, a = 3, if r = -3, a=-3
sum(n) = a(r^n - 1)/(r-1)
case1:
Sum(10) = 3(3^10 - 1)/(3-1)
= 3( 59048)/2 = 88572
case2:
sum(10) = -3( (-3)^10 - 1)/(-3-1) = 44286
checking the 2nd:
series = -3 + 9 - 27 + 81 - 243 + 729 - 2187 + 6561 - 19683 + 59049
= 44286
For the second question, why not just add them up?
You only have 4 terms!
otherwise: a = 10, r = 3
sum(4) = 10(3^4 - 1)/(3-1) = 400
Got it thanks so much :,)
To find the sum of the first 10 terms of the geometric sequence, you need to first determine the common ratio of the sequence.
The common ratio (r) can be found by dividing any term in the sequence by its preceding term. In this case, you can divide the fourth term (81) by the second term (9):
r = 81 / 9 = 9
Now that we know the common ratio is 9, we can find the first term (a) of the sequence by dividing the second term by the common ratio:
a = 9 / 9 = 1
Now that we have the first term (a = 1) and the common ratio (r = 9), we can use the formula for the sum of the first n terms of a geometric sequence:
Sn = a * (1 - r^n) / (1 - r)
In this case, we want to find the sum of the first 10 terms (n = 10). So, plugging in the values:
S10 = 1 * (1 - 9^10) / (1 - 9)
Simplifying the formula:
S10 = 1 * (-262143) / (-8)
S10 = 32768
Therefore, the sum of the first 10 terms of the given geometric sequence is 32768.