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If a(1),a(2),a(3),a(4) and a(5) are in A...

If `a_(1),a_(2),a_(3),a_(4)` and `a_(5)` are in AP with common difference `ne 0,` find the value of `sum_(i=1)^(5)a_(i) " when " a_(3)=2`.

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To solve the problem, we need to find the value of the sum \( S = a_1 + a_2 + a_3 + a_4 + a_5 \) given that \( a_3 = 2 \) and the terms \( a_1, a_2, a_3, a_4, a_5 \) are in an arithmetic progression (AP) with a common difference \( d \neq 0 \). ### Step-by-Step Solution: 1. **Understanding the Terms in AP**: In an arithmetic progression, the terms can be expressed in terms of the first term \( a_1 \) and the common difference \( d \): - \( a_1 = a_1 \) - \( a_2 = a_1 + d \) ...
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Knowledge Check

  • If a_(1), a_(2), a_(3), a_(4), a_(5) are consecutive terms of an arithmetic progression with common difference 3, then the value of |(a_(3)^(2),a_(2),a_(1)),(a_(4)^(2),a_(3),a_(2)),(a_(5)^(2),a_(4),a_(3))| is

    A
    0
    B
    27
    C
    81
    D
    162

  • If terms a_(1),a_(2),a_(3)...,a_(50) are in A.P and a_(6)=2, then the value of common difference at which maximum value of a_(1)a_(4)a_(5) occur is

    A
    `(3)/(5)`
    B
    `(8)/(5)`
    C
    `(2)/(5)`
    D
    `(2)/(3)`

  • If a_(1), a_(2), a_(3),…a_(n) are in A.P., where a_(i) gt 0 for all i, then the value of (1)/(sqrt(a_(1)) + sqrt(a_(2))) + (1)/(sqrt(a_(2)) + sqrt(3)) +...+ (1)/(sqrt(a_(n-1)) + sqrt(a_(n))) is

    A
    `(1)/(sqrt(a_(1)) + sqrt(a_(n)))`
    B
    `(1)/(sqrt(a_(1)) - sqrt(a_(n)))`
    C
    `(n)/(sqrt(a_(1)) - sqrt(a_(n)))`
    D
    `(n - 1)/(sqrt(a_(1)) + sqrt(a_(n)))`

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