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Arithmetic Progressions

Short Answer Type

61. Find the sums given below:
34 + 32 + 30 + . . . + 10

129 Views

62. Find the sums given below:
–5 + (–8) + (–11) + . . . + (–230)

154 Views

63.

In an AP
Given a = 5, d = 3, a_n=50, find n and S_n.

217 Views

64.

In an AP
given a = 7, a₁₃=35, find d and S₁₃.

458 Views

65.

In an AP
Given a₁₂ = 37, d = 3, find ‘a’ and S₁₂.

538 Views

66. Given a₃ = 75, S₁₀ = 120, find ‘d’ and a_10.

135 Views

67.
In an AP
Given d = 5, 5₉ = 75, find ‘a’ and ‘a’

Here, d = 5, S₉= 75
We know that,
$straight S subscript straight n equals straight n over 2 left square bracket 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d right square bracket therefore space space space space straight S subscript 9 space equals space 9 over 2 space straight x space left square bracket 2 straight a plus left parenthesis 9 minus 1 right parenthesis space straight x space 5 right square bracket rightwards double arrow space space space 75 space equals 9 over 2 straight x space left square bracket 2 straight a plus 8 space straight x space 5 right parenthesis rightwards double arrow 150 space equals space 9 cross times left square bracket 2 straight a plus 40 right square bracket rightwards double arrow 2 straight a plus 40 equals 150 over 9 equals 50 over 3 rightwards double arrow 2 straight a space equals space 50 over 3 minus 40 equals fraction numerator 50 minus 120 over denominator 3 end fraction rightwards double arrow space straight a equals fraction numerator negative 70 over denominator 3 cross times 2 end fraction equals negative 35 over 3 We space know space that. space straight a subscript straight n equals straight a plus left parenthesis straight n minus 1 right parenthesis straight d therefore space space space straight a subscript 9 equals negative 35 over 3 plus left parenthesis 9 minus 1 right parenthesis straight x 5 space space space space space space space space space equals negative 35 over 3 plus left parenthesis 9 minus 1 right parenthesis cross times 5 space space space space space space space space space space equals fraction numerator negative 35 over denominator 3 end fraction plus 40 space space space space space space space space space space space space space equals fraction numerator negative 35 plus 120 over denominator 3 end fraction equals 85 over 3 Hence comma space space space straight a equals fraction numerator negative 35 over denominator 3 end fraction space and space straight a subscript 9 equals 85 over 3$

182 Views

68. Find the sum of the series 5 + 7 + 9+ 10 + 13 + 13 + 17 + 16 +.........to 40 terms.

230 Views

69. Find four numbers in A .P. whose sum is 20 and the sum of whose squares is 180.

253 Views

70. Prove that no matter what the real numbers ‘a’ and ‘b’ are the sequence with nth term a + nb is always an A .P. what is the common difference ? What is the sum of the first 20 terms.

256 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

67. In an APGiven d = 5, 59 = 75, find ‘a’ and ‘a’

67.
In an AP
Given d = 5, 5₉ = 75, find ‘a’ and ‘a’