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Two given A.P.’s are 9, 7, 5, … and 24, 21, 18, … If nth term of both the .progressions are equal then find the value of n and n,h term.

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The first A.P. is 9, 7, 5,… 

Here, a = 9, d = 7- 9 = -2 

∴nth term = a + (n – 1)d 

= 9 + (n – 1) (-2) 

= 9 – 2n + 2 

= 11 – 2n 

The second A.P. is 24, 21, 18, … 

Here, a = 24, d = 21 – 24 = – 3 

∴ nth term = a + (n – 1)d 

= 24 + (n – 1) (-3) 

= 24 – 3n + 3 

= 27 – 3n 

Since, the nth terms of the two A.P.’s are equal. 

∴ 11 – 2n = 27 – 3n

∴ 3n – 2n = 27 – 11 

∴ n = 16 

∴ t16 = 9 + (16 – 1) (-2) 

= 9 + 15 × (-2) 

= 9 – 30 

∴ t16 = -21  

∴ The values of n and n term are 16 and -21 respectively.

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