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Question
Find the 31st term of an A.P. whose 10th term is 38 and the 16th term is 74.
Solution
The general term of an A.P. is given by
tn = a + (n – 1)d
Now, t10 = 38
`=>` a + 9d = 38 ...(i)
And t16 = 74
`=>` a + 15d = 74 ...(ii)
Subtracting (i) from (ii), we get
6d = 36
`=>` d = 6
Substituting d = 6 in (i), we get
a + 9 × 6 = 38
`=>` a + 54 = 38
`=>` a = –16
`=>` tn = –16 + (n – 1)(6)
`=>` t31 = –16 + 30 × 6
= –16 + 180
= 164
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