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Q.16 The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1.
Find the first term and the common difference.
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Answer:
Let a be the first term and d be the common difference.
The 4th term can be written as ‘a+3d’ and 7th term can be written as ‘a+6d’.
As per the question,
a+3d = 3a → 2a-3d=0
a+6d=2(a+2d)+1 →a+6d=2a+4d+1 →a-2d+1=0
Now solve the 2 quations, you will get:
d=2 & a=3
Hence, the first term is 3 and the common difference is 2.
The AP would be,
3,5,7,9,11,…..
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