Question

two A.P 63,65,67 ..... and 3,10,17...... the n the term are equal for both then find it​

Answer 1

Step-by-step explanation:

refer to the attachment

Answer 2

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✨We have given 63, 65, 67, …

➡️ a = 63

➡️ d = a 2 − a 1 = 65 − 63 = 2

${n}^{th} \:  term \: of \: this \: A.P. =  a_{n} = a + (n − 1) d$

$a_{n} = 63 + (n − 1) \\ = 63 + 2n − 2$

✨3, 10, 17, …

➡️ a = 3

$d =  a_{2} − a _{1} \: = 10 − 3 = 7$

➡️ n th term of this A.P. = 3 + (n − 1) 7

$a_{n} = 3 + 7n − 7$

$a_{n}  = 7n − 4 (2)$

❥It is given that, n th term of these A.P.s are equal to each other.

❥Equating both these equations,

❥we obtain,

➡️ 61 + 2n = 7n − 4 61 + 4 = 5n 5n = 65 n = 13

❥ Therefore, 13th terms of both these A.P.s are equal to each other.

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