Math - Arithmetic & Geometric

1) Given the terms a35 = 1238 and a70 = 1483 of an Arithmetic. Find the exact value of the term a105 a sequence and sum of sequence.

2) Given a3 = 99 and a5 = 891 of a Geometric. Find the exact value of the term a7 of the sequence and the sum of sequence.

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  1. 1.
    a+ 34d = 1238
    a+69d = 1483
    subtract them
    35d = 245
    d = 7
    then in the 1st equation:
    a + 238 = 1238
    a = 1000
    so term(105) = 1000 + 104(7) = 1728

    2.
    ar^2 = 99
    ar^4 = 891
    divide the 2nd by the third.
    r^2 = 9
    r = ±3
    in the 1st
    a(9) = 99
    a = 11

    then term(7)
    = ar^6
    = 11(3)^6 = 8019

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  2. Thanks a lot

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  3. An arithmetic sequence is represented in the following table. Enter the missing term of the sequence.

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  4. Math-ariyhmetic & geometric

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