The sum of the first three terms of an A.P. is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.

Let the three numbers be a - d, a, a + d. Given , sum of these terms = 33 ⇒ a - d + a + a + d = 33 ⇒ 3a = 33 ⇒ a = 11. Given, the product of the first and the third terms exceeds the second term by 29 ⇒ (a + d)(a - d) - a = 29 Putting the value of a = 11 we get, ⇒ (11 + d)(11 - d) - 11 = 29 ⇒ (11) 2 - d 2 - 11 = 29 ⇒ 121 - d 2 - 11 = 29 ⇒ 110 - d 2 = 29 ⇒ 110 - 29 = d 2 ⇒ d 2 = 81 ⇒ d = ⇒ d = +9, -9. ∴ a - d = 11 - 9 = 2 or 11 - (-9) = 20 and a + d = 11 + 9 = 20 or 11 + (-9) = 2. Hence, the A.P. is 2, 11, 20, ... or 20, 11, 2, ....

The sum of three numbers in A.P. is 3 and their product is -35. Find the numbers.

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The sum of three numbers in A.P. is 30 and the ratio of the first number to the third number is 3 : 7. Find the numbers.

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Find the sums given below:
(i) 34 + 32 + 30 + …. + 10
(ii) -5 + (-8) + (-11) + …. + (-230)

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Mathematics

The sum of the first three terms of an A.P. is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.

AP GP

Related Questions

The sum of three numbers in A.P. is 3 and their product is -35. Find the numbers.

The sum of three numbers in A.P. is 30 and the ratio of the first number to the third number is 3 : 7. Find the numbers.

Find the sums given below:
(i) 34 + 32 + 30 + …. + 10
(ii) -5 + (-8) + (-11) + …. + (-230)

Mathematics

The sum of the first three terms of an A.P. is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.

AP GP

Related Questions

The sum of three numbers in A.P. is 3 and their product is -35. Find the numbers.

The sum of three numbers in A.P. is 30 and the ratio of the first number to the third number is 3 : 7. Find the numbers.

Find the sums given below:(i) 34 + 32 + 30 + …. + 10(ii) -5 + (-8) + (-11) + …. + (-230)

Find the sums given below:
(i) 34 + 32 + 30 + …. + 10
(ii) -5 + (-8) + (-11) + …. + (-230)