If the coefficients of the three successive terms in the binomial expansion of (1+x)^n are in the ratio 1:7:42, then the first of these terms in the expansion is:

Let the three consecutive terms in the expansion of (1+x)^n be rth, (r+1)th and (r+2)th terms.

Tr = nCr-1xr-1
Tr+1 = nCrxr
Tr+2 = nCr+1xr+1

Given, nCr-1 : nCr : nCr+1 = 1 : 7 : 42

nCr-1 / nCr = 1/7 => 7nCr-1 = nCr
nCr / nCr+1 = 7/42 = 1/6 => 6nCr = nCr+1

Using the property nCr / nCr-1 = (n-r+1)/r

For 7nCr-1 = nCr => 7 = (n-r+1)/r => 7r = n-r+1 => n = 8r - 1
For 6nCr = nCr+1 => 6 = (n-r)/(r+1) => 6(r+1) = n-r => 6r+6 = n-r => n = 7r+6

Equating the values of n: 8r - 1 = 7r + 6 => r = 7
Therefore, n = 8(7) - 1 = 55

So, the three consecutive terms are 7th, 8th and 9th terms.
The first of these terms in the expansion is the 7th term.