Question

For what value of nth term of series 3,10,17......And63,65,67.... Are equal

Answer 1

For the 1st given AP i.e.
3, 10, 17, ...

a = 3
d = 7

$a_{n} = a + (n - 1)d \\ \\ a_{n} = 3 + (n - 1)7 \\ \\ a_{n} = 3 + 7n - 7 \\ \\ \bf \: a_{n} = 7n - 4 \: \: \: \: \: \: \: \: \: \: \: ...(i)$

For the 2nd given AP i.e.
63, 65, 67, ...

a = 63
d = 2

$a_{n} = a + (n - 1)d \\ \\ a_{n} = 63 + (n - 1)2 \\ \\ a_{n} = 63 + 2n - 2 \\ \\ \bf \: a_{n} = 61 + 2n \: \: \: \: \: \: \: \: \: \: \: \: ...(ii)$

On equating the values we get,

61 + 2n = 7n - 4

2n - 7n = - 4 - 61

- 5n = - 65

5n = 65

n = 13

Hence, for the 13th term, values of both the AP series will be equal.

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