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Question -

┬аIf the 3_rd┬аand the 9_th┬аterms of an A.P. are 4 and тИТ 8 respectively. Which term of this A.P. is zero.



Answer -

Given that,

3rd┬аterm, a3┬а= 4

and 9th┬аterm, a9┬а= тИТ8

We know that,

an┬а=┬аa+(nтИТ1)d

Therefore,

a3┬а=┬аa+(3тИТ1)d

4 =┬аa+2d┬атАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАж┬а(i)

a9┬а=┬аa+(9тИТ1)d

тИТ8 =┬аa+8d┬атАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАжтАж┬а(ii)

On subtracting equation┬а(i)┬аfrom┬а(ii), we will get here,

тИТ12 = 6d

d┬а= тИТ2

From equation┬а(i), we can write,

4 =┬аa+2(тИТ2)

4 =┬аaтИТ4

a┬а= 8

Let┬аnth┬аterm ofthis A.P. be zero.

an┬а=┬аa+(nтИТ1)d

0 = 8+(nтИТ1)(тИТ2)

0 = 8тИТ2n+2

2n┬а= 10

n┬а= 5

Hence, 5th┬аtermof this A.P. is 0.

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