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Arithmetic Progressions

Short Answer Type

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

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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.

Here, a₁₂ = 37, d= 3
We know that,
a_n= a + (n - 1)d
$rightwards double arrow$ a₁₂ = a + (12 - 1) x 3
$rightwards double arrow$ 37 = a + 11 x 3
$rightwards double arrow$ a = 37 - 33 = 4
And, $straight S subscript straight n space equals straight n over 2 straight x space left parenthesis straight a plus straight l right parenthesis therefore space space space straight S subscript 12 equals 12 over 2 straight x space left parenthesis 4 plus 37 right parenthesis space space space space space space equals space 6 straight x space 41 space equals space 246 Hence comma space space space straight a space equals space 4 and space straight S subscript 12 space equals space 246 end subscript$

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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’

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

65. In an APGiven a12 = 37, d = 3, find ‘a’ and S12.

65.
In an AP
Given a₁₂ = 37, d = 3, find ‘a’ and S₁₂.