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

Let the first term of the A.P. be a and common difference be d. By formula, a n = a + (n - 1)d Given, ⇒ 3rd term = 16 ⇒ a 3 = 16 ⇒ a + (3 - 1)d = 16 ⇒ a + 2d = 16 ..........(1) Given, 7th term exceeds the 5th term by 12. ⇒ a 7 - a 5 = 12 ⇒ a + (7 - 1)d - [a + (5 - 1)d] = 12 ⇒ a + 6d - [a + 4d] = 12 ⇒ a - a + 6d - 4d = 12 ⇒ 2d = 12 ⇒ d = = 6. Substituting value of d in equation (1), we get : ⇒ a + 2 × 6 = 16 ⇒ a + 12 = 16 ⇒ a = 16 - 12 = 4. A.P. : a, a + d, a + 2d, a + 3d, ........ ⇒ 4, 4 + 6, 4 + 2 × 6, 4 + 3 × 6, ..... ⇒ 4, 10, 16, 22, ........ Hence, the required A.P. is 4, 10, 16, 22, ........

How many multiples of 4 lie between 10 and 250?

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Mathematics

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

AP

Related Questions

How many multiples of 4 lie between 10 and 250?

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

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

The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.