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6 March, 13:28

Write each sum using summation notation

12 + 22 + 32 + 42 + ⋯ + 10000^2

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  1. 6 March, 13:55
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    50,00,70,000

    Step-by-step explanation:

    The given sequence is Arithmetic Progression.

    Arithmetic Progression is a sequence in which every two neighbor digits have equal distances.

    Here first we will find the number of terms

    For finding the nth term, we use formula

    aₙ = a + (n - 1) d

    where, aₙ = value of nth term

    a = First term

    n = number of term

    d = difference

    Now, In given sequence: 12, 22, 32, 42, ⋯, 100002

    a = 12, d = 10, n = ? and aₙ = 100002

    ∴ 100002 = 12 + (n - 1) * (10)

    ⇒ 99990 = 10 (n - 1)

    ⇒ n = 10000

    Now using the formula of Sum of Arithmetic Sequence,

    Sₙ = n:2[2a + (n - 1) d]

    ⇒ Sₙ = (10000:2) [2 * 12 + 9999 * 10]

    ⇒ Sₙ = 5000 [ 24 + 99990]

    ⇒ Sₙ = 5000 * 100014 = 50,00,70,000
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