For what value of n, are the nth terms of two APs: 63, 65, 67, ..... and 3, 10, 17, ........ equal?

Given, 1st AP : 63, 65, 67, ....... For 1st A.P., First term (a) = 63 and Common difference (d) = 65 - 63 = 2. nth term of 1st A.P. : = a + (n - 1)d = 63 + 2(n - 1) = 63 + 2n - 2 = 2n + 61. 2nd A.P. : 3, 10, 17, ......... First term (a 1 ) = 3 and Common difference (d 1 ) = 10 - 3 = 7. nth term of 2nd A.P. : = a 1 + (n - 1)d 1 = 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4. Since, nth term of both A.P.s are equal. ∴ 2n + 61 = 7n - 4 ⇒ 7n - 2n = 61 + 4 ⇒ 5n = 65 ⇒ n = = 13. Hence, 13th term of both the A.P.'s are equal.

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Mathematics

For what value of n, are the nth terms of two APs: 63, 65, 67, ….. and 3, 10, 17, …….. equal?

AP

Related Questions

How many three-digit numbers are divisible by 7?

How many multiples of 4 lie between 10 and 250?

Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.