An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

Let first term of A.P. be a and common difference be d. By formula, a n = a + (n - 1)d Given, Last term of A.P. = 106 and there are 50 terms in the A.P. ⇒ a 50 = 106 ⇒ a + (50 - 1)d = 106 ⇒ a + 49d = 106 .......(1) Given, 3rd term = 12 ⇒ a 3 = 12 ⇒ a + (3 - 1)d = 12 ⇒ a + 2d = 12 .......(2) Subtracting equation (2) from (1), we get : ⇒ a + 49d - (a + 2d) = 106 - 12 ⇒ a - a + 49d - 2d = 94 ⇒ 47d = 94 ⇒ d = = 2. Substituting value of d in equation (2), we get : ⇒ a + 2 × 2 = 12 ⇒ a + 4 = 12 ⇒ a = 12 - 4 ⇒ a = 8. 29th term = a 29 = a + (29 - 1)d = 8 + 28 × 2 = 8 + 56 = 64. Hence, 29th term = 64.

Check whether -150 is a term of the AP : 11, 8, 5, 2 …….

View Answer Bookmark Now

Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

View Answer Bookmark Now

If the 3rd and the 9th terms of an AP are 4 and -8 respectively, which term of this AP is zero?

View Answer Bookmark Now

The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

View Answer Bookmark Now

Mathematics

An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

AP

Related Questions

Check whether -150 is a term of the AP : 11, 8, 5, 2 …….

Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

If the 3rd and the 9th terms of an AP are 4 and -8 respectively, which term of this AP is zero?

The 17th term of an AP exceeds its 10th term by 7. Find the common difference.