Question

Write an A.P. whose first term is a and common difference is d in each of the following :
a=6, d=-3

Answer 1

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Terms of A.P whose first

term is a , and common difference

is d , is

a , a + d , a + 2d , a + 3d , ...,

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Here ,

First term = a = a1 = 6 ,

Common difference ( d ) = -3 ,

Second term = a + d

a2 = 6 - 3 = 3 ,

Third term = a + 2d

a3 = 6 + 2( -3 )

= 6 - 6 = 0

nth term = a +( n - 1 )d

an = 6 + ( n - 1 )( -3 )

= 6 - 3n + 3

= 9 - 3n

Therefore ,

Required A.P is

6 , 3 , 0 , ....., ( 9 - 3n )

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Answer 2

Sequence of terms in A.P. = a , a + d , a + 2d , a + 3d.....a + ( n - 1 )d
{ where n is the last term }



In the question , a = 6 and common difference = - 3


→ first term = a = 6


→ second term = a + d

second term = 6 + ( - 3 )

second term = 6 - 3

second term = 3


→ third term = a + 2d

third term = 6 + 2( - 3 )

third term = 6 - 6

third term = 0


→ nth term ( last term ) = a + ( n - 1 )d


nth term = 6 + ( n - 1 )( - 3 )

nth term = 6 - 3n + 3

nth term = 9 - 3n





Therefore,

Required AP is 6 , 3 , 0 .....9 - 3( last term )

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