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Sequences and series help please

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    Hi guys,

    Could some please check my answer for the first part of the question (in the attachment) and also help me with the second part.

    Thank you.
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    (Original post by Aty100)
    Hi guys,

    Could some please check my answer for the first part of the question (in the attachment) and also help me with the second part.

    Thank you.
    Yes, part (i) is right. Remember, it's just a_{n+1} = 3a_n - 1, so if we set n=2, we get: a_2 = 3a_1 - 1=  3(2) - 1 = 5 as you've said.

    Now for the next part, it's not an arithmetic sequence as there is no common difference. Instead, literally just calculate the next few terms and add them up manually.

    So \displaystyle \sum_{r=1}^{5} a_r = a_1 + a_2 + a_3 + a_4 + a_5

    That is, find a_4 = 3a_3 - 1, etc... and then just add them up.

    What I usually do for these questions is work out the value of more terms
    So in this case work out a1, a2, a3, a4 and a5
    Add them together to get the sum of all the terms
    I believe but I'm not 100% sure that the formula you are using for part 2 is for arithmetic sequences which have a common difference not recurrence relationships which is the question you're doing
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