I don't know where I got wrong with this problem. My answer is different from the answer sheet. To solve this problem, I used geometric sequence as $a, ar, ar^2 ..., ar^9$ and arithmetic sequence as $0, b, 2b,..., 9b$. Then I used the following equations to find a, r, and b, and from there I found the sum of the first 10 terms of the third sequence. $a+0=1$, $ar+b=1$, $ar^2+2b=2$
Given a geometric sequence with the first term a and common ratio r, where both a and r not equal to 0, and an arithmetic sequence with the first term 0, a third sequence 1,1,2... is formed by adding the corresponding terms of the 2 given sequences. Find the sum of the first 10 terms of the third sequence.