It is given that the sequence {xn} satisfies x1 = 0, xn+1 = xn + 1 + 21+xn for n = 1,2, . . . . . Then x31 is
Explanation:
x1 = 0 = 12 - 1
x2 = x1 + 1 + 21+x0 = 0 + 1 + 21+0 = 3 = 22 - 1
x3 = x2 + 1 + 21+x1 = 3 + 1 + 21+3 = 8 = 32 - 1
∴ xn = n2 - 1
⇒ x31 = 312 - 1 = 960
Hence, 960.
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