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Three numbers a, b, c, non-zero, form an...

Three numbers a, b, c, non-zero, form an arithmetic progression. Increasing a by 1 or increasing c by 2 results in a geometric progression. Then b equals :

A

16

B

14

C

12

D

10

Text Solution

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The correct Answer is:
To solve the problem, we need to follow these steps: ### Step 1: Understanding the Arithmetic Progression (AP) Given three numbers \(a\), \(b\), and \(c\) form an arithmetic progression, we know that: \[ 2b = a + c \quad \text{(1)} \]
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Knowledge Check

  • If a, b & 3c are in arithmetic progression and a, b & 4c are in geometric progression, then the possible value of (a)/(b) are

    A
    `{(2)/(3),2}`
    B
    `{(3)/(2),(1)/(2)}`
    C
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    D
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    A
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    B
    geometric progression
    C
    harmonic progression
    D
    None of these

  • Terms a 1 b are in Arithmetic Progression and terms 1 a b are in Geometric Progression Find a and b given a ne b

    A
    A)2,4
    B
    B)`-2,1`
    C
    C)`4,1`
    D
    D)`-2,4`

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