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# In an AP(iv) Given a3 = 15, S10 = 125, find d and a10. Q.3(4)

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In class 10th of arithmetic progressions who i solve this question in easy way of exercise 5.3 of the question is In an AP(iv) Given a3 = 15, S10 = 125, find d and a10.

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1. Given that,Â a3Â = 15,Â S10Â = 125

AsÂ we know, from the formula of the nth term in an AP,

anÂ =Â aÂ +(nâˆ’1)d,

Therefore, putting the given values, we get,

a3Â =Â a+(3âˆ’1)d

15 =Â a+2dÂ â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..Â (i)

Sum of the nth term,

SnÂ =Â n/2Â [2a+(n-1)d]

S10Â =Â 10/2Â [2a+(10-1)d]

125 = 5(2a+9d)

25 = 2a+9dÂ â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..Â (ii)

On multiplying equationÂ (i)Â byÂ (ii), we will get;

30 = 2a+4dÂ â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.Â (iii)

By subtracting equationÂ (iii)Â fromÂ (ii), we get,

âˆ’5 = 5d

dÂ = âˆ’1

From equationÂ (i),

15 =Â a+2(âˆ’1)

15 =Â aâˆ’2

aÂ = 17 = First term

a10Â =Â a+(10âˆ’1)d

a10Â = 17+(9)(âˆ’1)

a10Â = 17âˆ’9 = 8

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