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in Arithmetic Progression by (24.8k points)
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Write the value of n for which nth of the A.P.s 3, 10, 17, ... and 63, 65, 67, ... are equal.

1 Answer

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Best answer

Let nth term of A.P. 3,10,17,… be an 

And nth term of A.P. 63,65,67,…be an'

So,a1 = 3 and a2 = 10 

∴ d = a2 - a1 

= 10 - 3 

= 7 

And, 

a1' = 63 and a2' = 65 

∴ d' = a2' - a1' = 65 - 63 = 2 

Now, 

an = a1+(n-1)d 

= 3+(n-1)7 

= 3+7n-7 

= 7n-4 

And, 

an'=a1'+(n-1)d' 

= 63+(n-1)2 

= 63+2n-2 

= 2n+61 

Now,

It is given that an = an'

∴ 7n-4 = 2n+61 

∴ 7n-2n = 61+4 

∴ 5n = 65 

∴ n = 13

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