Question

15 For what value of n, are the nth terms of two APs: 63, 65, 67,... and 3, 10, 17,... equal?
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Answer 1

Answer:

AP = 63,65,67,..

a = 63

d = 2

an = a + (n-1)d

= 63 + (n-1)2

= 63 + 2n - 2

= 61 + 2n

AP = 3,10,17,...

a' = 3

d' = 7

a'n = a' + (n-1)d'

= 3 + (n-1)7

= 3 + 7n -7

= -4 + 7n

ATQ,

an = a'n

61 + 2n = -4 + 7n

61 + 4 = 7n - 2n

65 = 5n

n = 65/5

n = 13

The 13th terms of both the APs are equal.

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Answer 2

Answer:

AP=63,65,67,..

a=63

d=2

an=a+(n-1)d

=63+(n-1)2

=63+2n-2

=61+2n

AP=3,10,17,..

a'=3

d'=7

a'n=a+(n+1)d'

=3+(n-1)7

=3+7n-7

=-4+7n

ATQ,

an=a'n

61+2n=-4+7n

61+4=7n-2n

65=5n

n=13

the 13th terms of both the APs are equal.