Question

Question 9 If the 3 rd and the 9 th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero.

Class 10 - Math - Arithmetic Progressions Page 106

Answer 1

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Answer 2

General term or nth term of A.P

The general term or nth term of A.P is given by an = a + (n – 1)d, where a is the first term, d is the common difference and n is the number of term.---------------------------------------------------------------------------------------------------

Solution:

Given:

a3 = 4
a9 = −8

We know that,
an = a + (n − 1) d

a3 = a + (3 − 1) d
4 = a + 2d … (i)

a9 = a + (9 − 1) d
−8 = a + 8d … (ii)

On subtracting equation (i) from (ii), we get,
−12 = 6d
d = −2
From equation (i), we get,
4 = a + 2 (−2)
4 = a − 4
a = 8

Let the nth term of an A.P. is zero.
an = a + (n − 1) d

0 = 8 + (n − 1) (−2)
0 = 8 − 2n + 2
2n = 10
n = 5

Hence, 5th term of this A.P. is 0.

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