algebra

The fifth term of an A.P exceeds twice the second term by 1.The tenth term exceeds twice the fourth term by 3.
Find:1.the first term.
2.the common difference.
3.the sum of first twenty five terms.

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  1. Xn = a + (n-1)d

    X5 = a + 4 d

    X5 - 1 = 2 [ a + d ]

    X10 - 3 = 2 [ a + 3 d ]
    but X10 = a+9d

    so

    a + 4 d - 1 = 2 a + 2 d
    a = 2 d - 1

    a + 9 d - 3 = 2 a + 6 d
    a = 3 d -3

    combine
    3 d - 3 = 2 d - 1
    d = 4

    You take it from there.

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