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Question
If the nth term of the A.P. 58, 60, 62, .... is equal to the nth term of the A.P. –2, 5, 12, …., find the value of n.
Solution
In the first A.P. 58, 60, 62, ....
a = 58 and d = 2
tn = a + (n – 1)d
⇒ tn = 58 + (n – 1)2 ...(i)
In the first A.P. –2, 5, 12, ....
a = –2 and d = 7
tn = a + (n – 1)d
`\implies` tn= –2 + (n – 1)7 ...(ii)
Given that the nth term of first A.P is equal to the nth term of the second A.P.
`\implies` 58 + (n – 1)2 = –2 + (n – 1)7 …[From (i) and (ii)]
`\implies` 58 + 2n – 2 = –2 + 7n – 7
`\implies` 65 = 5n
`\implies` n = 13
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