# Arithmetic Progressions

#### Question 15:

For what value of *n*, are the *n*^{th} terms of
two APs 63, 65, 67, and 3, 10, 17, … equal

#### Answer:

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) 2 = 63
+ 2*n* − 2

*a*_{n} = 61 + 2*n* (1)

3, 10, 17, …

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