Question

A sequence of numbers U1, U2, U3 ..., Un satisfies the relation Un+1 = Un + (1/2)^2 for all integers n >_1 If U1 = 1, find: the values of U2, U3 and U4 an expression for Un in terms of n. the value of Un for large values of n

Answer 1

arithmetic sequence ?
a = 1
d = 1/2 * 1/2 = 1/4
Tn = a + (n-1) d
Un = 1 + (n-1)* 1/4

Answer 2

To solve that:
Un+1 = Un¬+(1/2)2
When n =1
U2=1+1/4
U2=5/4
When n=2
U3=5/4 + 1/4
U3=6/4
When n=3
U4=6/4+1/4
U4=7/4
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Answer 3

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