Class 11

Math

Algebra

Binomial Theorem

Assertion :No three consecutive binomial coefficient can be in G.P. & H.P.

Reason :Three consecutive binomial coefficients are in A.P.

- Both Assertion & Reason are individually true & Reason is correct explanation of Assertion,
- Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion,
- Assertion is true but Reason is false,
- Assertion is false but Reason is true.

$_{n}C_{r−1},_{n}C_{r},_{n}C_{r+1}$

Then it must follow a relationship

$(n−2r)_{2}=n+2$

We know that binomial coefficients are part of pascals triangle, and we can observe that no 3 consecutive integers in a row form G.P or H.P.