Mathematics
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 tn = 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.
AP
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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 4 is the correct option.
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