Question

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If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively, then which term of this A.P is zero ?
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Answer 1

Answer:

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Given that,

3rd term, a3 = 4

and 9th term, a9 = −8

We know that, the nth term of AP is;

an = a + (n − 1) d

Therefore,

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 will get here,

−12 = 6d

d = −2

From equation (i), we can write,

4 = a + 2 (−2)

4 = a − 4

a = 8

Let nth term of this A.P. be 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

Answer 2

Given that,

3rd term, a3 = 4

and 9th term, a9 = −8

We know that, the nth term of AP is;

an = a + (n − 1) d

Therefore,

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 will get here,

−12 = 6d

d = −2

From equation (i), we can write,

4 = a + 2 (−2)

4 = a − 4

a = 8

Let nth term of this A.P. be 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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