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Question 8
Find the 20th term of the AP whose 7th term is 24 less than the 11th term, first term being 12.

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Solution

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 = 12 + 19 × 6 = 126

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