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Arithmetic Progressions

Short Answer Type

201. If S_n, the sum of first n terms of an A .P. is given by S_n = 3n² – 4n, then find its nth term.

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202. If S_n, the sum of first n terms of an A .P. is given by S_n = Sn² + 3n, then find its nth term.

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203. The sum of 4th and 8th terms of an A .P. is 24 and sum of 6th and 10th terms is 44. Find A .P.

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204. The sum of 5th and 9th terms of an A .P. is 72 and the sum of 7th and 12th terms is 97. Find the A .P.

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205. If 4/5, a, 2 are three consecutive terms of an A .P., then find the value of a.

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206. Which term of the A .P. 3, 15, 27, 39,.....will be 120 more than its 21 st term.

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207. The sum of first six terms of an A .P. is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first and the thirteen term of the A .P.

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208. For what value of k, are the numbers x, 2x + k and 3x + 6 three consecutive terms of an A .P.?

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209.

Which term of AP; 121, 117, 113,.....is its first negative terms ?
(a) 31 (b) 33 (c) 32 (d) 34

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210. If last term of an AP is – 10 and first term and common difference are 100, –2 then the no. of terms ‘n’ will be : (a) 55 (b) 56 (c) 57 (d) 58

a subscript n equals a plus left parenthesis n minus 1 right parenthesis d rightwards double arrow negative 10 equals 100 plus left parenthesis n minus 1 right parenthesis space cross times space minus 2 rightwards double arrow fraction numerator negative 110 over denominator negative 2 end fraction equals n minus 1 rightwards double arrow n equals 56

Ans. (b)

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