The sum of 3rd&7th term of an ap is 6 the product is 8.find the sum of first 20th term of ap.
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Given:-
The sum of 3rd term and 7th term
=>a+2d+a+6d = 6
=>2a+8d = 6
After common taking
a + 4d = 3
a=3-4d ..................….......(1)
Their product is
(a+2d)×(a+6d) = 8 .........…(2)
Putting value of a = 3–4d in equation (2) to get
=>(a+2d)×(a+6d) = 8
=>(3–4d+2d)×(3–4d+6d) =8
=>(3–2d)×(3+2d) = 8
=>9–4d^2 = 8
=>4d^2 = 9-8
=>4d^2 = 1
=>d^2 = 1/4
=>d = 1/2.
From (1) a = 3–4d
a=> 3–4×1/2
a=>3-2
a=> 1
The sum of the first 20 terms
Sum of 16 terms = (n/2)[2a+(n-1)d]
= (20/2)[2×1 + (20–1)×1/2]
= 10[2+19/2]
= 10×23/2
= 230/2
=115
Hence,
The sum of first 20 term is 115
Hope it helps you
Given:-
The sum of 3rd term and 7th term
=>a+2d+a+6d = 6
=>2a+8d = 6
After common taking
a + 4d = 3
a=3-4d ..................….......(1)
Their product is
(a+2d)×(a+6d) = 8 .........…(2)
Putting value of a = 3–4d in equation (2) to get
=>(a+2d)×(a+6d) = 8
=>(3–4d+2d)×(3–4d+6d) =8
=>(3–2d)×(3+2d) = 8
=>9–4d^2 = 8
=>4d^2 = 9-8
=>4d^2 = 1
=>d^2 = 1/4
=>d = 1/2.
From (1) a = 3–4d
a=> 3–4×1/2
a=>3-2
a=> 1
The sum of the first 20 terms
Sum of 16 terms = (n/2)[2a+(n-1)d]
= (20/2)[2×1 + (20–1)×1/2]
= 10[2+19/2]
= 10×23/2
= 230/2
=115
Hence,
The sum of first 20 term is 115
Hope it helps you
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