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प्रश्न
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.
उत्तर
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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