Question

If the nth terms of two A.P.s 23, 25, 27, ... and 5, 8, 11, 14, ... are equal,then find the value of n.
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Answer 1

Answer:

n=18

Step-by-step explanation:

SInce one AP starts from 23 with increment of 2,

nth term=23+2n

In other AP, values start from 5 with increment of 3

So, nth term=5+3n

From the question,

       23+2n=5+3n

       3n-2n=23-5

        n=18

Answer 2

Answer:

$23,25 ,27,... \: .is \: ap \: no 1 \\ </p><p>5,8,11,14 .... \: ..is \: Ap \: no 2 \\ </p><p></p><p></p><p>1st Ap \\ </p><p>a= 23 \\ </p><p>d=2 \\ \underline{{a}(n) = 23 + (n - 1)2 \: \: \: \: \: \: ....... \boxed {1}}\: \\ \\ 2nd \: a.p. \\ a = 5 \\ d = 3 \\ \underline {a(n) = 5 +( n - 1)3 \: \: \: \: \: \: ...... \boxed{2}} \\ from \: 1 \: and \: 2 \: \\ 23 + ( n- 1)2 = 5 + ( n- 1)3 \\ \\ 23 - 5 = (n - 1)3 - (n - 1)2 \\ \\ 18 = (n - 1) \\ \\ \\ n = 18 + 1 \\ n = 19 \\ \\ \green{\boxed{ \red{n = 19}}}$

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