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?

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

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APPEARS IN

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