Let a n = 1 2 n − 1 for n = 1 , 2 , 3 , . . .Write out the first three terms of these sequencesa) b n = a n + 1b) c n = a n + 3c) d n = a 2 n

Question

Let       a    n    =      1          2      n        −  1 for   n  =  1  ,  2  ,  3  ,  .  .  .Write out the first three terms of these sequencesa)       b    n    =      a    n    +  1b)       c    n    =      a    n    +  3c)       d    n    =      a          2      n

mallol3i · Accepted Answer

1) Given       b    n    =      a    n    +  1      b    n    =      1    2    n  −  1  +  1      b    n    =      1    2    nFor the first term:   n  =  1      b    1    =      1    2    (  1  )      b    1    =      1    2  For the second term:   n  =  2      b    2    =      1    2    (  2  )      b    2    =  1For the third term:   n  =  3      b    3    =      1    2    (  3  )      b    3    =      3    2  Thus, three terms are:       1    2    ,  1  ,      3    2  2) Given       c    n    =      a    n    +  3      c    n    =      1    2    n  −  1  +  3      c    n    =      1    2    n  +  2For   n  =  1      c    1    =      1    2    (  1  )  +  2      c    1    =      5    2  For   n  =  2      c    2    =      1    2    (  2  )  +  2      c    2    =  1  +  2  =  3For   n  =  3      c    3    =      1    2    (  3  )  +  2      c    3    =      3    2    +  2      c    3    =      7    2  Thus, three terms are:       5    2    ,  3  ,      7    2

Jase Howe · Accepted Answer

Part c      d    n    =            a      n        2        d    n    =      1    2    (      1    2    n  −  1  )      d    n    =      1    4    n  −      1    2  If   n  =  1, we have      d    1    =      1    4    (  1  )  −      1    2        d    1    =            1      −      2        4        d    1    =            −      1        4  If   n  =  2, we have      d    2    =      1    4    (  2  )  −      1    2        d    2    =      1    2    −      1    2        d    2    =  0If   n  =  3, we have      d    3    =      1    4    (  3  )  −      1    2        d    3    =      3    4    −      1    2        d    3    =      1    4  Thus, the three terms:             −      1        4    ,  0  ,      1    4

Let a n </msub> = 1 2 n </mrow> </mfrac>

Answered question

Answer & Explanation

New Questions in Algebra I