Q. 17 D4.0( 2 Votes )

# For what value of n are the nth term of the following two A.P's the same. Also find this term63, 65, 67, ... and 3, 10, 17, ...

1st AP = 63, 65, 67, ...

Here, a = 63, d = 65 – 63 = 2

and 2nd AP = 3, 10, 17, ...

Here, a = 3, d = 10 – 3 = 7

According to the question,

63 + (n – 1)2 = 3 + (n – 1)7

63 + 2n – 2 = 3 + 7n – 7

61 + 2n = 7n – 4

65 = 7n – 2n

5n = 65

n = 13

13th term of the given AP’s are same.

Now, we will find the 13th term

We have,

an = a + (n – 1)d

a13 = 63 + (13 – 1)2

a13 = 63 + 12 × 2

a13 = 63 + 24

a13 = 87

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