sum of the terms pf arithmetic progression?

1) if a boy saved 25 pesos on the first day. 27 pesos the second day, 29 pesos the third day, and so on how many days will it take him to 5550 pesos?

2) a ticket raffle consists of 20 prizes. The first prize is 25,000 pesos and each successive prize is 500 pesos less than the preceding prize. what is the value of the 19th place?

i need solutions :)

Update:

of not pf :)

then..

i need a better solution because i cannot understand

oooppsss its not 5550 its 850 :D hehe

Update 2:

its not 850 its 880 and its answers is 20 days in number 1 but i need the solution and in number 2 i, the answer is 16,000 pesos

1 Answer

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  • 1 decade ago
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    1) This is an arithmetic sequence, modelled by the formula

    Sn = n/2 * (2a1 + (n-1)d), where

    - Sn is the sum of the number of terms, which is 880

    - a1 is the initial value, which is 25

    - n is the number of terms, which we are trying to find

    - d is the difference between consecutive terms, which is 2.

    This gives

    880= (n/2) * (50 +2(n-1))

    880= (n/2) * (48 + 2n)

    n^2 + 24n - 880 = 0

    n = 20

    Therefore it will take him 20 days to make 5550 peso.

    2) Tn = a + d(n-1)

    Tn = 25000 - 500 (19-1)

    Tn = 16000

    Therefore, the value of the 19th place is 16000 pesos.

    These are just formulas for finding terms or sums of arithmetic sequences. Your book should give an explanation of these. If you need more information, look at the following two links:

    http://www.ltcconline.net/greenl/courses/103B/seqS...

    http://www.mathguide.com/lessons/SequenceArithmeti...

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