If the ratio between the two middle terms in the expansion of is , find .
We know that the value of is 3, so there will be 4 terms in this expansion. The two middle terms are the second and third terms. The formula for the ratio of two consecutive terms is
Because we are dealing with the second and third terms, the value of is 2, that of is 3, that of the first term is 1 and that of the second is .
Substitute these values into the formula and set it equal to the given ratio. Remember that the first value in the ratio is for the second term of the expansion and the second value in the ratio is for the third term. Then solve for .
The value of is 2.