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The 16th term of an AP is three times the 5th term.If the 12th term is 20 more the 7th term.Find the first term and the common difference​

User Smita More
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1 Answer

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Answer:

  • First term = 6
  • Common difference= 4

Solution:

Let's take the first term as a and the common difference be d

The formula to find the nth term of an arithmetic progression is given by :

  • an = a + ( n - 1 ) d

According to question, we have :

  • 16th term of an AP is three times the 5th term.

a16 = 3 ( a5 )

a + ( 16 - 1 )d = 3 ( a + ( 5 - 1 )d )

a + 15d = 3 ( a + 4d )

a + 15d = 3a + 12d

15d - 12d = 3a - a

3d = 2a

2a = 3d

a = 3d/2ㅤ‎ㅤ‎ㅤ⸻ ( 1 )

  • And, the 12th term is 20 more the 7th term.

a12 - ( a7 ) = 20

a + ( n - 1 )d -( a + ( n - 1 )d ) = 20

a + ( 12 - 1 )d - + a + ( 7 - 1 )d ) = 20

a + 11d - ( a + 6d ) = 20

a - a + 11d - 6d = 20

5d = 20

d = 20/ 5

d = 4

  • Using equation ( 1 )

a = 3d / 2

a = ( 3 × 4 ) / 2

a = 12 / 2

a = 6

User BlueNC
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