已知数列{an}满足a1=1，an+1=an+2n，则a10=．

Question

已知数列{a_n}满足a₁=1，a_n+1=a_n+2ⁿ，则a₁₀=______．

Answer 1

∵数列{a_n}满足a₁=1，a_n+1=a_n+2ⁿ，
∴a_n=a₁+（a₂-a₁）+…+（a_n-a_n-1）=1+2¹+2²+…+2^n-1=(2n−1)/(2−1)=2ⁿ-1．（n∈N^*）．
∴a₁₀=2¹⁰-1=1023．
故答案为：1023．