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

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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)

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63.

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

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64.

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

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65.

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

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

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67.

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

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

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

Solution not provided.
Ans. –1,3,7, 11

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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.

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