___, ___, 17, ___, ___, 29 Work out the missing terms. Work out the nth term

The sequence is of the form

9 ,   13 , 17 , 21 , 25 ,29

Step-by-step explanation:

Explanation:-

Step(i):-

Given sequence   , ___, __17_ ,___,___ 29

The third term = 17

          a + (3-1)d = 17

          a + 2 d = 17 ...(i)

The sixth term = 29

      a + (6-1)d =29

      a + 5 d  = 29 ...(ii)

solving (i) and (ii) equations

Subtracting (i) and (ii) equations , we get

 a + 2 d -a -5 d = 17 -29

   - 3 d = - 12

       d =4

Substitute 'd' =4 in equation (i)

   a + 2 d = 17

  a + 2(4) =17

  a = 17 -8 = 9

Step(ii):-

The arithmetic sequence

            a ,   a+d ,   a+2 d  ,  a+ 3 d , a+ 4 d , a+5 d

            9  , 9 + 4, 9 +2 (4) , 9+3(4) , 9 +4(4) , 9+5(4)

             9 ,   13 , 17 , 21 , 25 ,29

Conclusion:-

The sequence is of the form

9 ,   13 , 17 , 21 , 25 ,29

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step-by-step explanation:

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step-by-step explanation: