I need someone to check and see if I have it right...if not..can you please correct I think i did 7 decimals instead of six. How do you do 6 decimals?
Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer: r = 1/3
Show work in this space. Each term is the previous term divided by 3 or times 1/3
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.
Answer: 1.4999745
Show work in this space. S = 1(1 - (1/3)10)/(1 - (1/3)) = (1 - 1/59049)/(2/3) = 1.4999745
c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments.
Answer: 1.4999971
Show work in this space. S = 1(1 - (1/3)12)/(1 - (1/3)) = (1 - 1/531441)/(2/3) = 1.4999971
2006-11-04 11:40:45 · 5 answers · asked by othe1220 1 in Science & Mathematics ➔ Mathematics
Those are the right numbers. As you suspected they have too many decimal places, however. To have them correct to 6 decimal places, look at the 7th decimal place. If this is 5 or more, round the 6th decimal up one, otherwise leave it the same and just drop all the numbers after it.
So for a) the answer would be 1.499975 and for b) it would be 1.499997.
2006-11-04 12:00:13 · answer #1 · answered by thegreatdilberto 2 · 0⤊ 0⤋
Hi. A is correct. Round off your 7 decimal numbers to 6. Looks like an asymptotic approach to 1.5, so the rounding is important. The rest looks good.
2006-11-04 11:48:45 · answer #2 · answered by Cirric 7 · 0⤊ 0⤋
Your numbers are good, since it matches all the geometric formulas such as An = A1*r^n (1 = 1*1; 1/3 = 1*r^1; 1/9 = 1*r^2) or the sum S = [A1 ( 1 - r^n)]/1 - r where A1 is your first number and r is the ratio.
2006-11-04 11:50:44 · answer #3 · answered by VrmpX 2 · 0⤊ 0⤋
b) The answer to this, to 8 decimals, is 1.49997460.
To round this to 6 decimals, notice that the 7th decimal (6) is greater than or equal to 5, so you round up the 6th decimal (4) to a 5.
Final answer is : 1.499975
c) To 8 decimals, the answer is 1.49999718.
The 7th decimal (1) is less than 5, so you leave the 6th decimal (7) as it is.
Final answer is : 1.499997
2006-11-04 12:07:09 · answer #4 · answered by falzoon 7 · 0⤊ 0⤋
a. is correct.
b. is correct (1.499974) from 1.499974597
c. is almost correct, the last digit is 2 because of rounding up
i.e. 1.499997177 becomes 1.4999972
But the question requires 6 decimals, so the answer is really
1.499997
2006-11-04 11:52:28 · answer #5 · answered by mathpath 2 · 0⤊ 0⤋