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Question
4th term of an A.P. is equal to 3 times its first term and 7th term exceeds twice the 3rd term by 1. Find the first term and the common difference.
Solution
The general term of an AP is given by tn = a + (n – 1)d
Now t4 = 3 × a
`=>` a + 3d = 3a
`=>` 2a – 3d = 0 ...(i)
Next t7 + 2 × t3 = 1
`=>` a + 6d – 2(a + 2d) = 1
`=>` a + 6d – 2a – 4d = 1
`=>` – a + 2d = 1 ...(ii)
Multiplying (ii) by 2, we get
–2a + 4d = 2 ...(iii)
Adding equation (i) and (iii), we get
d = 2
Substituting the value of d in (ii), we get
–a + 2 × 2 = 1
`=>` –a + 4 = 1
`=>` a = 3
Hence a = 3 and d = 2
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