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For What Value of N, the Nth Terms of the Arithmetic Progressions 63, 65, 67, ... and 3, 10, 17, ... Are Equal? - Mathematics

Sum

For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... are equal?

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Solution

Here, we are given two A.P. sequences. We need to find the value of n for which the nth terms of both the sequences are equal. We need to find n

So let us first find the nth term for both the A.P.

First A.P. is 63, 65, 67 …

Here,

First term (a) = 63

Common difference of the A.P. (d) = 65 - 63 =2

Now, as we know,

an = a + (n - 1) d

So, for nth term,

`a_n = 63 + (n-1)2`
      = 63 + 2n - 2

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

Second A.P. is 3, 10, 17 …

Here,

First term (a) = 3

Common difference of the A.P. (d) =10-3 =7

Now, as we know,

an = a+ (n-1)d

So, for nth term,

an = 3 + (n-1) 7 

     = 3 + 7n  - 7

     = - 4 + 7 n                ...................(2)

Now, we are given that the nth terms for both the A.P. sequences are equal, we equate (1) and (2),

61 + 2n = - 4 + 7n

2n - 7n = -4 - 61

     - 5n = - 65

         `n =(-65)/(-5)`

           n = 13

Therefore, n = 13 

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.4 | Q 28 | Page 25
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