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Thread: [SOLVED] Arithmetic Sequence Problem

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    Exclamation [SOLVED] Arithmetic Sequence Problem

    An arithmetic sequence has a common difference of d. If the sum of 20 terms is 25 times the first term, find, in terms of d, the sum of 30 terms.
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    Quote Originally Posted by amanda.chonghalliday View Post
    An arithmetic sequence has a common difference of d. If the sum of 20 terms is 25 times the first term, find, in terms of d, the sum of 30 terms.
    $\displaystyle S_n = \frac{n}{2} \cdot (2a+(n-1)d)$

    where a is the first term
    n is the number of terms
    d is the common difference

    $\displaystyle S_{20} = \frac{20}{2} \cdot (2a + (20-1)d) = 25a$

    $\displaystyle 10 \times (2a + 19d) = 25a$

    $\displaystyle 20a + 190d = 25a \rightarrow a = 38d$

    $\displaystyle S_{30} = \frac{30}{2} \times (2a + (30-1)d)$

    $\displaystyle S_{30} = 15 \times (2 \times 38d + 29d)$

    $\displaystyle S_{30} = 15 \times 105d = 1575d$
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