The sum of first 10 terms of an ap is - 150 and the sum of its next 10 terms is -550. Find the AP.
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The sum of first 10 terms of an ap is - 150 and the sum of its next 10 terms is -550. Find the AP.
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Let to sum of first 10 terms of an ap =Snthe sum of its next 10 terms of an ap =sn'
S₁₀ = -150
S₁₀ + S'₁₀ = S₂₀
Given :-
S'₁₀ = -550
Therefore ,
S₂₀ = -150 -550
= -700
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Lets form two linear equations and solve it :-
S₁₀ = -150
n = 10
Sn = n/2 [ 2a + (n-1)d]
-150= 10/2 [ 2a + 9d ]
-150 = 5 [ 2a + 9d ]
-30 = 2a + 9d
2a + 9d = -30 (Equation 1)
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S₂₀ = -700
numbers of terms n = 20
Sn = n/2 [ 2a + (n-1)d]
-700 = 20/2 [ 2a + 19d ]
-700 = 10 [ 2a + 19d ]
-70 = 2a + 19d
2a + 19d = -70 (-equation 2)
solving equations 1 and 2 :-
(2) - (1)
2a + 19d = -70
2a + 9d = -30
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10d = -40
d = -40/10 = -4
Substitute the value of d in equation;
2a + 9d = -30
2a -36 = -30
2a = -30+36
a = 6/2 = 3
a=3
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According to the question:-
first term (a )= 3
Common difference ( d)= -4
Arithmetic progressions:
3,-1,-5,-9
Thanks!!!