Let a₁, a₂, ......., a₁₀ be an AP with common difference $$-$$ 3 and b₁, b₂, ........., b₁₀ be a GP with common ratio 2. Let c_k = a_k + b_k, k = 1, 2, ......, 10. If c₂ = 12 and c₃ = 13, then $$\sum\limits_{k = 1}^{10} {{c_k}} $$ is equal to _________.

If $${\log _3}2,{\log _3}({2^x} - 5),{\log _3}\left( {{2^x} - {7 \over 2}} \right)$$ are in an arithmetic progression, then the value of x is equal to _____________.

If the value of

$${\left( {1 + {2 \over 3} + {6 \over {{3^2}}} + {{10} \over {{3^3}}} + ....upto\,\infty } \right)^{{{\log }_{(0.25)}}\left( {{1 \over 3} + {1 \over {{3^2}}} + {1 \over {{3^3}}} + ....upto\,\infty } \right)}}$$

is $$l$$, then $$l$$² is equal to _______________.

The sum of all the elements in the set {n$$\in$$ {1, 2, ....., 100} | H.C.F. of n and 2040 is 1} is equal to _____________.