Directions: A series is given with one missing term. Choose the correct option from the given ones that will complete the series.

-45, ?, -270, -540, -1620, -3240, -9720

The correct option is -90.

To find the missing term in the given number series, let us analyze the relationship between consecutive numbers starting from the known terms:

$-270\times 2=-540$

$-540\times 3=-1620$

$-1620\times 2=-3240$

$-3240\times 3=-9720$

By examining these operations, we observe a clear alternating multiplication pattern: each term is multiplied alternately by 2 and then by 3 to produce the next term in the sequence.

Applying this pattern from the start of the series:

Step 1: Multiply the first term by 2 to find the missing second term (?):

$-45\times 2=-90$

Step 2: Multiply the second term (-90) by 3 to verify the third term:

$-90\times 3=-270$

This confirms that the missing number completing the series is indeed -90.