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प्रश्न
Find the 20th term of the AP whose 7th term is 24 less than the 11th term, first term being 12.
उत्तर
Let the first term, common difference and number of terms of an AP are a, d and n, respectively.
Given that,
First term (a) = 12
Now by condition,
7th term (T7) = 11th term (T11) – 24 ...[∵ nth term of an AP, Tn = a + (n – 1)d]
⇒ a + (7 – 1)d = a + (11 – 1)d – 24
⇒ a + 6d = a + 10d – 24
⇒ 24 = 4d
⇒ d = 6
∴ 20th term of AP,
T20 = a + (20 – 1)d
= 12 + 19 × 6
= 126
Hence, the required 20th term of an AP is 126.
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