Help me with 7(ii)
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Question 7 : ( i )
Given sequence is - 2 / 4 , - 4 / 8 , - 8 / 16...
= > - 2 / 4, ( 2 / 2 )( - 2 / 4 ), ( 2 / 2 )( - 4 / 8 )....
If we see, all the terms of given sequence are in GP( geometric progression ), since all the sequence is constantly being multiplied by 2 / 2 . Thus, 2 / 2 is the common ratio of the terms. And therefore next terms should be
= > - 8 / 16 x common ratio
= > - 8 / 16 x 2 / 2
= > - 16 / 32
Therefore the required next term of the sequence is - 16 / 32.
And, similarly, other two terms are - 16 / 32 x 2 / 2 i.e. - 32 / 64 and - 32 / 64 x 2 / 2 i.e. - 64 / 128
Hence, required next three terms of the sequence are - 16 / 32, - 32 / 64, - 64 / 128.
( ii ) :
Given sequence is - 1 / 2 , 0 , 1 / 2 ....
This sequence belongs to arithmetic progressions, as it is common difference [ 0 - ( - 1 / 2 ) = 0 + 1 / 2 = 1 / 2 ] ,which is continuously being added to the upcoming term of the sequence.
And, due to this, next term should be
= > 1 / 2 + 1 / 2
= > ( 1 + 1 ) / 2
= > 2 / 2
= > 1
Hence the required next term is 1
And, the other two terms are 1 + 1 / 2 i.e. 3 / 2 and 3 / 2 + 1 / 2 i.e. 2.
Hence required next three terms are 1, 3 / 2 and 2.