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Question
Which term of the A.P. 3, 10, 17, .......... will be 84 more than its 13th term?
Solution
A.P. is 3, 10, 17, ..........
Here, a = 3, d – 10 – 3 = 7
T13 = a + 12d
= 3 + 12 × 7
= 3 + 84
= 87
Let nth term is 84 more then its 13th term
∴ Tn = 84 + 87 = 171
`\implies` a + (n – 1)d = 171
`\implies` 3 + (n – 1) × 7 = 171
`\implies` (n – 1) × 7 = 171 – 3 = 168
`\implies` n – 1 = `(168)/(7)` = 24
`\implies` n = 24 + 1
`\implies` n = 25
∴ 25th term is the required term.
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