A.P + GP \neq A.G.P

Algebra Level 4

Let A={a1,a2,,an}A=\{a_1, a_2, \ldots, a_n\} be a set of the first nn terms of an arithmetic progression. Similarly, let B={b1,b2,,bn}B=\{b_1, b_2, \ldots, b_n\} be a set of the first nn terms of a geometric progression.

If a new set C=A+B={a1+b1,a2+b2,,an+bn}C=A+B=\{a_1+b_1, a_2+b_2, \ldots, a_n+b_n\} and the first four terms of CC are {0,0,1,0},\{0, 0, 1, 0\}, what is the 11th11^\text{th} term of C?C?

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