Assertion (A): The 10th term from the end of the A.P. 17, 14, 11, … −40 is −11.
Reason (R): The nth term of an A.P. is given by t_n = a + (n − 1)d.
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.

Question

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

Reason (R): The nth term of an A.P. is given by t_n = a + (n − 1)d.

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.

KnowledgeBoat · Accepted Answer

Given, a = 17 an = -40 d = 14 - 17 = -3 We know that, ⇒ an = a + (n - 1)d ⇒ -40 = 17 + (n - 1)(-3) ⇒ -40 - 17 = (n - 1)(-3) ⇒ -57 = (n - 1)(-3) ⇒ = (n - 1) ⇒ 19 = n - 1 ⇒ n = 19 + 1 ⇒ n = 20. The A.P. has 20 terms. The 10th term from the end is the (n - 10 + 1)th term from the beginning = 20 - 10 + 1 = 11th term from beginning. ⇒ an = a + (n - 1)d ⇒ a11 = 17 + (11 - 1)(-3) = 17 + 10(-3) = 17 - 30 = -13. Assertion (A) is false. The standard and correct formula for finding the nth term of an Arithmetic Progression. an = a + (n - 1)d Reason (R) is true. A is false, R is true Hence, option 2 is the correct option.

Mathematics

AP

Related Questions

If the sum of n terms of an arithmetic progression S_n = n² - n, then the third term of the series is :
2
4
6
9

Mathematics

AP

Related Questions

If the sum of n terms of an arithmetic progression Sn = n2 - n, then the third term of the series is :2469

If the sum of n terms of an arithmetic progression S_n = n² - n, then the third term of the series is :
2
4
6
9