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26 October, 04:59

An arithmetic sequence has first term a = 5 and common difference d = 4. how many terms of this sequence must be added to get 4185?

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Answers (2)
  1. 26 October, 05:11
    0
    General Equation : an = a1 + d (n - 1)

    Find the nth sequence:

    Given that a1 = 5 and d = 4,

    an = 5 + 4 (n - 1)

    an = 5 + 4n - 4

    an = 4n + 1

    Find an:

    Given that Sn = 4185, find an

    sn = (a + an) / 2

    4185 = (5 + an) / 2

    5 + an = 8370

    an = 8370 - 5

    an = 8365

    Find n:

    We know that an = 8365, find n

    an = 4n + 1

    8365 = 4n + 1

    4n = 8365 - 1

    4n = 8364

    n = 2091

    Answer: 2091 terms
  2. 26 October, 05:15
    0
    Given that in arithmetic sequence a=5 and common difference, d=4. Thus the number of terms of this sequence that must be added to attain 4185 will be found as follows:

    the explicit formula for arithmetic sequence is given by:

    sn=n/2 (2a + (n-1) d)

    where n is the number of terms:

    thus plugging in the values we get:

    4185=n/2 (2*5 + (n-1) 4)

    solving for n we get:

    8370 = (10+4n-4)

    8370 = (6+4n)

    4n=8364

    n=8364/4

    n=2091

    thus the number of terms will be:

    2091
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