Question

for what value of n , are the nth term of two APs 63, 65 ,67,..... and 3,10,17,.... equal?

Answer 1

Hi ,

1 ) 63 , 65 , 67 , ... is an A.P

a = 63,

Common difference ( d ) = a2 - a1

d = 65 - 63 = 2

nth term = a + ( n - 1 ) d

an = 63 + ( n - 1 ) 2

= 63 + 2n - 2

= 2n + 61 ------( 1 )

2 ) 3 , 7 , 10 , ... is an A.P

a = 3 ,

d = 7 - 3 = 4

an = 3 + ( n - 1 ) 4

= 3 + 4n - 4

= 4n - 1 ----( 2 )

According to the problem given ,

( 1 ) = ( 2 )

2n + 61 = 4n - 1

61 + 1 = 4n - 2n

62 = 2n

62 /2 = n

31 = n

n = 31

If n = 31 then nth terms of two AP are

equal.

I hope this helps you.

:)

Answer 2

Hope my answer helps you ✌️✌️✌️ .....

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