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

Let first term of A.P. be a and common difference be d. By formula, a n = a + (n - 1)d Given, 3rd term = 4 ⇒ a 3 = 4 ⇒ a + (3 - 1)d = 4 ⇒ a + 2d = 4 ........(1) Given, 9th term = -8 ⇒ a 9 = -8 ⇒ a + (9 - 1)d = -8 ⇒ a + 8d = -8 ........(2) Subtracting equation (1) from (2), we get : ⇒ a + 8d - (a + 2d) = -8 - 4 ⇒ a - a + 8d - 2d = -12 ⇒ 6d = -12 ⇒ d = = -2. Substituting value of d in equation (1), we get : ⇒ a + 2 × -2 = 4 ⇒ a - 4 = 4 ⇒ a = 4 + 4 = 8. Let nth term of the A.P. be zero. ⇒ a n = a + (n - 1)d ⇒ 0 = 8 + (n - 1) × (-2) ⇒ 0 = 8 - 2n + 2 ⇒ 2n = 10 ⇒ n = = 5. Hence, 5th term of the A.P. is zero.

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

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

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

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Which term of the AP : 3, 15, 27, 39,……. will be 132 more than its 54th term ?

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Mathematics

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

AP

Related Questions

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

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

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

Which term of the AP : 3, 15, 27, 39,……. will be 132 more than its 54th term ?