# Find the 20th term of the AP whose 7th term is 24 less than the 11th term, first term being 12. - Mathematics

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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 given condition,

7th term (T7) = 11th term (T11) – 24  ........[∵ nth term of an AP, Tn = a + (n – 1 )d]

⇒ a + (7 – 1)d = a + (11 – l)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.

Concept: Arithmetic Progression
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 5 Arithematic Progressions
Exercise 5.3 | Q 8 | Page 52
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