Year: 1, 2, 3, 4, 5
Sale:.48,1.032,2.198,4.726,10.208
(in millions)
-If the sales growth pattern continues, what will be the sales for ABC Company in year 12?
-What will be the total sales for ABC Company for years 1 through 12?
I know that this is a geometric sequence with a common ratio of 2.13
Since you have figured r, and a = 0.48,
Tn = 0.48*2.13^(n-1)
T12 = 0.48*2.13^11 = 1965.25
S12 = 0.48(1-2.13^12)/(1-2.13) = 3703.98
To find the sales for ABC Company in year 12, we can use the common ratio and the sales in year 5.
Step 1: Calculate the common ratio
The common ratio is the ratio between consecutive terms in the sequence. In this case, the common ratio is 2.13.
Step 2: Find the sales in year 5
The sales in year 5 is given as 10.208 million.
Step 3: Calculate the sales in year 12
To find the sales in year 12, we need to multiply the sales in year 5 by the common ratio raised to the power of (12-5) since year 12 is seven years after year 5.
Sales in year 12 = Sales in year 5 * (Common ratio)^(12-5)
Sales in year 12 = 10.208 * (2.13)^(12-5)
Now, we can calculate the sales in year 12.
Sales in year 12 = 10.208 * (2.13)^7 = 10.208 * 127.926837
Sales in year 12 ≈ 1307.05 million
Therefore, if the sales growth pattern continues, the sales for ABC Company in year 12 will be approximately 1307.05 million.
To find the total sales for ABC Company for years 1 through 12, we need to add the sales for each year from year 1 to year 12.
Total sales for years 1 through 12 = Sale in year 1 + Sale in year 2 + Sale in year 3 + Sale in year 4 + Sale in year 5 + Sale in year 6 + Sale in year 7 + Sale in year 8 + Sale in year 9 + Sale in year 10 + Sale in year 11 + Sale in year 12
Total sales for years 1 through 12 = 0.48 + 1.032 + 2.198 + 4.726 + 10.208 + (10.208 * 2.13) + (10.208 * 2.13^2) + (10.208 * 2.13^3) + (10.208 * 2.13^4) + (10.208 * 2.13^5) + (10.208 * 2.13^6) + (10.208 * 2.13^7)
Now, we can calculate the total sales for years 1 through 12.
To find the sales for year 12 using the geometric sequence, we need to first find the common ratio. The common ratio is the ratio between two consecutive terms in the sequence. In this case, the common ratio is 2.13.
To find the sales for year 12, we can use the formula for the nth term of a geometric sequence:
\[a_n = a_1 \cdot r^{(n-1)}\]
where \(a_n\) is the nth term, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the number of terms.
Using the given information, the first term is 0.48 (sales for year 1) and the common ratio is 2.13. We want to find the sales for year 12, so we substitute \(n = 12\) into the formula:
\[a_{12} = 0.48 \cdot 2.13^{(12-1)}\]
Calculating this, we get:
\[a_{12} = 0.48 \cdot 2.13^{11}\]
Therefore, the sales for ABC Company in year 12 would be approximately equal to the calculated value of \(a_{12}\).
To find the total sales for ABC Company for years 1 through 12, we need to sum up the sales for each year. We can use the formula for the sum of the first \(n\) terms of a geometric sequence:
\[S_n = \frac{{a_1 (1 - r^n)}}{{1 - r}}\]
where \(S_n\) is the sum of the first \(n\) terms, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the number of terms.
In this case, we want to find the sum of the sales for years 1 through 12, so we substitute \(n = 12\) into the formula:
\[S_{12} = \frac{{0.48 (1 - 2.13^{12})}}{{1 - 2.13}}\]
Calculating this, we get:
\[S_{12} = \frac{{0.48 (1 - 2.13^{12})}}{{-1.13}}\]
Therefore, the total sales for ABC Company for years 1 through 12 would be approximately equal to the calculated value of \(S_{12}\).