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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.

Here a = 5, d = 3, a_n = 50
We know that, a_n = a + (n – 1 )d
⇒ 50 = 5 + (n – 1) x 3
⇒ 50 – 5 = 3 x (n – 1)
⇒ 45 = 3 x (n – 1)
$rightwards double arrow space space straight n space minus space 1 space equals space 45 over 3 equals 15 rightwards double arrow space space straight n space equals space 15 space plus space 1 space equals space 16 And comma space space space space space straight S subscript straight n space equals space straight n over 2 left square bracket 2 straight a space plus space left parenthesis straight n minus 1 right parenthesis straight d right square bracket therefore space space space straight S subscript 16 equals 16 over 2 left square bracket 2 cross times 5 plus left parenthesis 16 minus 1 right parenthesis cross times 3 right square bracket space$
= 8 x [ 10 + 15 x 3]
= 8 x 10 + 45
= 8 x 55 = 440
Hence, n = 16
and S_n=S₁₆= 440

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’

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

63. In an APGiven a = 5, d = 3, an =50, find n and Sn.

63.
In an AP
Given a = 5, d = 3, a_n=50, find n and S_n.