Math, asked by prajnadevadiga, 11 months ago

First term of an AP is 2 and sum of first 5 terms is one fourth the sum of next five terms.Show that 20th term is -112 and find sum of first 20 terms ​

Answers

Answered by smitamahapatra2090
3

Answer:

S_{20} = -1100

Step-by-step explanation:

a = 2

S_{5} = 1/4 × S_{6 - 10}

⇒ 5/2( a + a_5 ) = 1/4 × 5/2 × ( a_6 + a_{10} )

⇒ a + a + 4d = 1/4( a + 5d + a + 9d)

⇒ 2a + 4d = 1/4( 2a + 14d )

⇒ 4(2a + 4d) = 2a + 14d

⇒ 8a + 16d = 2a + 14d

⇒ 6a + 2d = 0

⇒ 6(2) + 2d = 0

⇒ 12 + 2d = 0

⇒ 2d = -12

⇒ d = -6

A_{20} = a + 19d = 2 + 19(-6) = 2 - 114 = -112

S_{20} = 20/2 ( a + a_{20} )

     = 10( 2 - 112 )

     = 10(-110)

     = -1100

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