Find the sum of the counting numbers from 1 to 25 inclusive. In other words, if S = 1 + 2 + 3 + … + 24 + 25, find the value of S.

Question

Find the sum of the counting numbers from 1 to 25 inclusive. In other words, if S = 1 + 2 + 3 + … + 24 + 25, find the value of S.

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Thu Hương 3 years 2021-07-22T04:10:24+00:00 2 Answers 32 views 0

Answers ( )

  1. bonexptip
    0
    2021-07-22T04:11:34+00:00
    Reply

    Answer:

    s= 325

    Step by step explanation:

    Add all numbers 1 to 25 to get 325.

  2. Nho
    0
    2021-07-22T04:11:39+00:00
    Reply

    Answer:

    325

    Step-by-step explanation:

    You must have heard about Arithmetic Progressions (AP)

    Arithmetic progressions are a series of numbers such that every successive number is the sum of a constant number and the previous number.

    Our very own counting numbers form AP

    For example :-

    2 = 1 + 1

    3 = 2 + 1

    4 = 3 + 1

    The number in bold (1) is that constant number which is added to a number to form its successive number.

    To find the sum of series forming AP, we use the formula :-

    sum = \frac{n}{2} \{ a + a _{n} \}

    here,

    • n is the number of terms
    • a is the first number of the series
    • an is the last number of the series

    So we’ll use all this information to find the sum of continuous numbers from 1 to 25 where 1 is the first term(a) and 25 is the last(an).

    and n is 25

    S = \frac{25}{2}\{ 1 +25\}

    = \frac{25 \times 26}{2}

    = 25 \times 13

    = 325

    So, the value of S comes out to be 325.

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