Question 1127070
x,2x+1,11 are three consecutive terms of an arithmetic sequence. Calculate(i) x.(ii) the 30th term.
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x,2x+1,11 are the first three terms of an arithmetic sequence. Calculate(i) x.(ii) the 30th term.
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x + d = 2x + 1  —>  d = x + 1   (1)
(2x + 1) + d = 11  —>  d = 10 - 2x  (2)<br>

Set (1) equal to (2):   x + 1 = 10 - 2x
                                  3x = 9
                                    x = 3<br>

d = x + 1 —>  d = 4<br>

(i)  {{{highlight( x=3 ) }}}<br>

(ii) To find an answer, it must be assumed that the three terms given are the FIRST three terms (or at least their position m must be given) of the sequence (the problem statement does not provide sufficient information).  
      {{{ a[1] = 3 }}}
     {{{ a[2] = 3+4 = 7 }}}
     {{{ a[3] = 3+2*4 = 11 }}} 
       ...
     {{{ a[n] = 3 + (n-1)*4 }}} <br>

Plugging in n=30:
     {{{ a[30] = 3 + (29)*4 = 3+116 = highlight( 119 ) }}}