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  1. Asked: In:

    Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 1², 5², 7², 73, . . .

    Best Answer
    sargam jha

    1², 5², 7², 73, . . a₂ - a₁ = 5² -1² = 25 - 1 = 24 a₃ - a₂ = 7² - 5² = 49 - 25 = 24 a₄ - a₃ = 73 - 7² = 73 - 49 = 24 The difference between the successive terms are same Hence, it is an A.P. Common difference = 24, next three terms of this AP is as follows: Fifth term a₅ = a₄ + d = 73 + 24 = 97 SixtRead more

    1², 5², 7², 73, . .
    a₂ – a₁ = 5² -1² = 25 – 1 = 24
    a₃ – a₂ = 7² – 5² = 49 – 25 = 24
    a₄ – a₃ = 73 – 7² = 73 – 49 = 24
    The difference between the successive terms are same Hence, it is an A.P.
    Common difference = 24, next three terms of this AP is as follows:
    Fifth term a₅ = a₄ + d = 73 + 24 = 97
    Sixth term a₆ = a₅ + d = 97 + 24 = 121
    Seventh term a₇ = a₆ + d = 121 + 24 = 145

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  2. Asked: In:

    Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 1², 3², 5², 7², . . .

    Best Answer
    sargam jha

    1², 3², 5², 7², . . a₂ - a₁ = 3² -1² = 9 - 1 = 8 a₃ - a₂ = 5² - 3² = 25 - 9 = 16 a₄ - a₃ = 7² - 5² = 49 - 25 = 24 The difference between the successive terms are not same Hence, it is not an A.P.

    1², 3², 5², 7², . .
    a₂ – a₁ = 3² -1² = 9 – 1 = 8
    a₃ – a₂ = 5² – 3² = 25 – 9 = 16
    a₄ – a₃ = 7² – 5² = 49 – 25 = 24
    The difference between the successive terms are not same Hence, it is not an A.P.

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    • 2
  3. Asked: In:

    Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. √3, √6, √9 , √12, . . .

    Best Answer
    sargam jha

    √3, √6, √9 , √12, . . . a₂ - a₁ = √6 - √3 a₃ - a₂ = √9 - √6 = 3 - √6 a₄ - a₃ = √12 - √9 = 2√3 - 3 The difference between the successive terms are not same Hence, it is not an A.P.

    √3, √6, √9 , √12, . . .
    a₂ – a₁ = √6 – √3
    a₃ – a₂ = √9 – √6 = 3 – √6
    a₄ – a₃ = √12 – √9 = 2√3 – 3
    The difference between the successive terms are not same Hence, it is not an A.P.

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  4. Asked: In:

    Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 3, 3 + √2 , 3 + 2√2 , 3 + 3√2 , . . .

    Best Answer
    sargam jha

    3, 3 + √2 , 3 + 2√2 , 3 + 3√2 , . . . a₂ - a₁ = 3 +√2 - 3 = √2 a₃ - a₂ = 3 + 2√2 - (3 +√2) = √2 a₄ - a₃ = 3 + 3√2 - (3 + 2√2) = √2 The difference between the successive terms are same Hence, it is an A.P. Common difference = 4, next three terms of this AP is as follows: Fifth term a₅ = a₄ + d = 3 +Read more

    3, 3 + √2 , 3 + 2√2 , 3 + 3√2 , . . .
    a₂ – a₁ = 3 +√2 – 3 = √2
    a₃ – a₂ = 3 + 2√2 – (3 +√2) = √2
    a₄ – a₃ = 3 + 3√2 – (3 + 2√2) = √2
    The difference between the successive terms are same Hence, it is an A.P.
    Common difference = 4, next three terms of this AP is as follows:
    Fifth term a₅ = a₄ + d = 3 + 3√2 + √2 = 3 + 4√2
    Sixth term a₆ = a₅ + d = 3 +4√2 + √2 = 3 + 5√2
    Seventh term a₇ = a₆ + d = 3 + 5√2 + √2 = 3 + 6√2 .

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  6. Asked: In:

    Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. – 10, – 6, – 2, 2, . . .

    Best Answer
    sargam jha

    – 10, – 6, – 2, 2, . . . a₂ - a₁ = - 6 - (-10) = 4 a₃ - a₂ = - 2 - (-6) = 4 a₄ - a₃ = 2 - (- 2) = 4 The difference between the successive terms are same Hence, it is an A.P. Common difference = 4, next three terms of this AP is as follows: Fifth term a₅ = a₄ + d = 2 + 4 = 6 Sixth term a₆ = a₅ + d =Read more

    – 10, – 6, – 2, 2, . . .
    a₂ – a₁ = – 6 – (-10) = 4
    a₃ – a₂ = – 2 – (-6) = 4
    a₄ – a₃ = 2 – (- 2) = 4
    The difference between the successive terms are same Hence, it is an A.P.
    Common difference = 4, next three terms of this AP is as follows:
    Fifth term a₅ = a₄ + d = 2 + 4 = 6
    Sixth term a₆ = a₅ + d = 6 + 4 = 10
    Seventh term a₇ = a₆ + d = 10 + 4 = 14 .

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    • 2
  7. Asked: In:

    Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. – 1.2, – 3.2, – 5.2, – 7.2, . . .

    Best Answer
    sargam jha

    – 1.2, – 3.2, – 5.2, – 7.2, . . . a₂ - a₁ = - 3.2 - (- 1.2) = - 2.0 a₃ - a₂ = - 5.2 - (-3.2) = - 2.0 a₄ - a₃ = 7.2 - (- 5.2) = - 2.0 The difference between the successive terms are same Hence, it is an A.P. Common difference = - 2.0, next three terms of this AP is as follows: Fifth term a₅ = a₄ + dRead more

    – 1.2, – 3.2, – 5.2, – 7.2, . . .
    a₂ – a₁ = – 3.2 – (- 1.2) = – 2.0
    a₃ – a₂ = – 5.2 – (-3.2) = – 2.0
    a₄ – a₃ = 7.2 – (- 5.2) = – 2.0
    The difference between the successive terms are same Hence, it is an A.P.
    Common difference = – 2.0, next three terms of this AP is as follows:
    Fifth term a₅ = a₄ + d = 7.2 + 2.0 = – 9.2
    Sixth term a₆ = a₅ + d = – 9.2 – 2.0 = – 11.2
    Seventh term a₇ = a₆ + d = – 11.2 – 2.0 = – 13.2 .

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    • 2
  8. Asked: In:

    Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 2, 5/2, 3, 7/2, . . .

    Best Answer
    sargam jha

    – 1.2, – 3.2, – 5.2, – 7.2, . . . a₂ - a₁ = - 3.2 - (- 1.2) = - 2.0 a₃ - a₂ = - 5.2 - (-3.2) = - 2.0 a₄ - a₃ = 7.2 - (- 5.2) = - 2.0 The difference between the successive terms are same Hence, it is an A.P. Common difference = - 2.0, next three terms of this AP is as follows: Fifth term a₅ = a₄ + dRead more

    – 1.2, – 3.2, – 5.2, – 7.2, . . .
    a₂ – a₁ = – 3.2 – (- 1.2) = – 2.0
    a₃ – a₂ = – 5.2 – (-3.2) = – 2.0
    a₄ – a₃ = 7.2 – (- 5.2) = – 2.0
    The difference between the successive terms are same Hence, it is an A.P.
    Common difference = – 2.0, next three terms of this AP is as follows:
    Fifth term a₅ = a₄ + d = 7.2 + 2.0 = – 9.2
    Sixth term a₆ = a₅ + d = – 9.2 – 2.0 = – 11.2
    Seventh term a₇ = a₆ + d = – 11.2 – 2.0 = – 13.2 .

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    • 2