Question

f the quarterly seasonal indices for the second, third and fourth quarter are 0.54,0.97, and 1.40, then the First quarter seasonal index is:

Answer 1

To find the first quarter seasonal index when you have the seasonal indices for the other quarters, you can use the fact that the sum of all seasonal indices for a year should equal the number of quarters (which is 4 in this case).

Given the indices:
- Q2 = 0.54
- Q3 = 0.97
- Q4 = 1.40

Let Q1 be the seasonal index for the first quarter. The equation will look like this:

\[
Q1 + Q2 + Q3 + Q4 = 4
\]

Substituting the known values into this equation:

\[
Q1 + 0.54 + 0.97 + 1.40 = 4
\]

Now, add the indices for Q2, Q3, and Q4:

\[
0.54 + 0.97 + 1.40 = 2.91
\]

So now we can rewrite the equation:

\[
Q1 + 2.91 = 4
\]

Now, solve for \( Q1 \):

\[
Q1 = 4 - 2.91 = 1.09
\]

Therefore, the seasonal index for the first quarter is **1.09**.