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:
Solutions · 1
Official solution
\[\frac{{}^nC_r}{{}^nC_{r+1}}=\frac17,\qquad\frac{{}^nC_{r+1}}{{}^nC_{r+2}}=\frac{7}{42}\]
Solving these two ratio equations simultaneously gives r=6, so the first of these terms is the 7th term.