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Arithmetic Progressions

Question
CBSEENMA10007520

In the following APs, find the missing terms in the boxes.

negative 4 comma space square comma square comma space square comma square comma space 6





Solution

Let the common difference of the given A. P. be d.
                         a = - 4
                  6th term = 6
rightwards double arrow space space minus 4 plus left parenthesis 6 minus 1 right parenthesis straight d space equals 6
space space space space space space space space space space space space space left square bracket because space straight a subscript straight n equals straight a plus open vertical bar straight n minus 1 close vertical bar straight d right square bracket
rightwards double arrow space space minus 4 plus 5 straight d equals 6
rightwards double arrow space space space space space space 5 straight d equals 6 plus 4
rightwards double arrow space space space space space space space 5 straight d space equals space 10
rightwards double arrow space space space space space space space space straight d equals 10 over 5
rightwards double arrow space space space space space space space space straight d space equals space 2
Therefore,
      Second term = -4 + 2 = -2
      Third term = -2 + 2 = 0
      Fourth term = 0 + 2 = 2
and, Fifth term = 2 + 2 = 4
Hence, the missing terms in the boxes are
box enclose negative 2 end enclose comma space box enclose 0 comma space box enclose 2 comma space box enclose 4