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
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Answer:
= -1100
Step-by-step explanation:
a = 2
= 1/4 ×
⇒ 5/2( a + ) = 1/4 × 5/2 × ( )
⇒ 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 + 19d = 2 + 19(-6) = 2 - 114 = -112
= 20/2 ( a + )
= 10( 2 - 112 )
= 10(-110)
= -1100
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