Final answer:
To forecast the first quarter sales, the expected annual sales of 4600 are divided by 4 to find the average quarterly sales, which is then multiplied by the seasonal index of 1.05, resulting in a first quarter forecast of 1207.5.
Step-by-step explanation:
To forecast the sales for the first quarter using a seasonal index, you would take the total sales expected for the year and divide by the number of quarters to determine the average sales per quarter. Then, you adjust this average by the seasonal index for the particular quarter you are interested in. In this case, the total annual sales are expected to be 4600. Divided by 4, this gives an average of 1150 per quarter. To find the first quarter forecast, you multiply this average by the seasonal index for the first quarter, which is 1.05.
First Quarter Sales Forecast = Average Quarterly Sales × Seasonal Index
First Quarter Sales Forecast = 1150 × 1.05 = 1207.5
Therefore, the forecast for the first quarter is 1207.5 or 1207.5 thousand if the original figure was in thousands.