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Arithmetic Progressions

Short Answer Type

91. If the sum of first n terms of an A .P. is given by S_n = 5n² + 3n. Find the nth term of the A .P.

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92. If the sum of first n terms of an A .P. is given by S_n = 5n² + 3n. Find the nth term of the A .P.

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93. How many terms are there in the A .P. whose first and 6th terms are –13 and 12 respectively and the sum of the term is 132?

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94. In an A .P. if the 12th term is –13 and the sum of first four terms is 24. What is the sum of first 10 terms.

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95. The sum of first eight terms of an A .P. is 0 and its sixth term is 6. Find the first term and common difference.

Solution not provided.
Ans. a = -14, d= 4

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96. The third term of an A .P. is 7 and seventh term exceeds three times the third term by 2. Find its first term, the common difference and the sum of first 20 terms.

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97.

Find the sums given below :

(i) 101 + 99 + 97 +.........+ 47
(ii) 5 + 8 + 11 +.........+ 185
(iii) 2 + 4 + 6 +.........+ 200
(iv) 3 + 11 + 19 +.........+ 803

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98.

Find the sum of the following A.P.s : (i) 36, 31,.........to 10 terms.
(ii) a + b, a – b, a – 3b..........to 22 terms.
(iii) (x – y)², (x² + y²), (a + y)²,........to n terms.

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99.

In an A .P.
(i) given a = 5, d = 3, T_n = 50, find n and S_n.
(ii) given a = 6, d = 4, T_n = 50 find n and S_n.
(iii) given a = 7, d = 6, T_n = 43, find n and S_n.

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100. Find the sum of all odd numbers between 100 and 200.

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