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Mathematics : Arithmetic Progressions

Short Answer Type

71.

Write the expression a_n – a_k for the A .P. : a, a + d, a + 2d, .......... Hence find the common difference of the A .P. for which

(i) 11th term is 5 and 13th term is 79.
(ii) a₁₀ – a₅ = 200.
(iii) 20th term is 10 more than the 18th term.

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72. Three numbers are in A .P. if the sum of these numbers is 27 and the product 585, find the numbers.

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73. The sum of three consecutive terms in an A .P. is 18 and their product is 192. Find the numbers.

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74. Which term of the A .P. : 121, 117, 113..........is its first negative term.

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75. The sum of the third and the seventh terms of an A .P. is 6 and their product is 8. Find the sum of first sixteen terms of the A .P.

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76. The angles of a triangle are in A .P. if the greatest angle is double the least. Find all the angles.

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77. The sale of entrance tickets of an exhibition was Rs. 6500 on the first day and showed a decrease of Rs. 110 on every succeeding day. If the overall expenses of the exhibition are Rs. 1000 per day, find when the exhibition ceases to be profitable.

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78. The sum of n terms of an A .P. whose first term is 5 and common difference is 36 is equal to the sum of 2n terms of another A.P., whose first term is 36 and common difference is 5. Find n.

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79. Find the A .P. whose nth term is a_n = 10– 3n.

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80. Find V so that 2n + 1, n² + n + 1 and 3n² – 3n + 3 are consecutive terms of an A .P.

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