Question

Assertion (A): The 10th term from the end of the A.P. 17, 14, 11, ....... –40 is –11.

Reason (R): nth term of an A.P. is given by \(t_{n} = a + (n - 1)d\).

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is false, but R is true.

Explanation:

Assertion: With \(a = 17\), \(d = -3\), \(l = -40\): \(-40 = 17 - 3(n - 1) \Rightarrow n = 20\) terms, so the 10th term from the end \(= l - (10 - 1)d = -40 - 9(-3) = -13 \neq -11\). Hence A is false. 

Reason: \(t_n = a + (n - 1)d\) is a correct and valid formula for the nth term of an A.P., so R is true.