Question For what value of n, are the nth terms of two A.Ps 63, 65, 67,.... and 3, 10, 17,.... equal?
Video Explanation
Explanatory Answer
The nth term of an arithmetic progression, an = a1 + (n – 1)d
The first series is 63, 65, 67, ………
The first term of the series is 63 and its common difference is 2.
Therefore, the nth term of the first AP = 63 + (n – 1)2
The second series is 3, 10 , 17 ………
The first term of the series is 3 and its common difference is 7
The nth term of the second AP = 3 + (n – 1)7
The nth term of both the APs are equal
Therefore, 63 + (n – 1)2 = 3 + (n – 1)7
60 = 5(n – 1)
60 = 5n – 5
65 = 5n
n = 13
The 13th term of both the arithmetic progressions will be same.
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