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Question

The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP.                                                          [CBSE 2013]


Solution

Let a be the first term and d be the common difference of the AP. Then,

a19=3a6                                Givena+18d=3a+5d            an=a+n-1da+18d=3a+15d3a-a=18d-15d         
2a=3d                         .....1

Also,
a9=19               Givena+8d=19               .....2

From (1) and (2), we get
3d2+8d=193d+16d2=1919d=38d=2

Putting d = 2 in (1), we get
2a=3×2=6a=3

So,
a2=a+d=3+2=5a3=a+2d=3+2×2=7,...

Hence, the AP is 3, 5, 7, 9, ... .

Mathematics
RS Aggarwal (2018)
Standard X

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