Q. 17 A5.0( 3 Votes )

# For what value of n are the nth term of the following two A.P's the same. Also find this term13, 19, 25, ... and 69, 68, 67, ...

1st AP = 13, 19, 25, …

Here, a = 13, d = 19 – 13 = 6

and 2nd AP = 69, 68, 67, …

Here, a = 69, d = 68 – 69 = –1

According to the question,

13 + (n – 1)6 = 69 + (n – 1)(–1)

13 + 6n – 6 = 69 – n + 1

7 + 6n = 70 – n

6n + n = 70 – 7

7n = 63

n = 9

9th term of the given AP’s are same.

Now, we will find the 9th term

We have,

an = a + (n – 1)d

a9 = 13 + (9 – 1)6

a9 = 13 + 8 × 6

a9 = 13 + 48

a9 = 61

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