║⊕QUESTION⊕║
Mathematics is the most beautiful and most powerful creation of the human spirit.
↓
CLASS 11
SEQUENCES AND SERIES
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How many terms of the series 3 + 7 + 11 + 15 + .... must be taken to make the sum 820?
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║⊕QUESTION⊕║
Mathematics is the most beautiful and most powerful creation of the human spirit.
↓
CLASS 11
SEQUENCES AND SERIES
↑
How many terms of the series 3 + 7 + 11 + 15 + .... must be taken to make the sum 820?
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Solution
a=3
d=7-3=4
let the number of terms is n now...
s(n)=[n(2×3+(n-1))]/2
820 × 2 =n (6+4n-4)
1640 = 2n +4n^2
2n^2+n-820=0
2n^2+41n-40n-820=0
n(2n+41)-20(2n+41)=0
(2n+41) (n-20)=0
taking only positive value of n(cause n is a natural number)n=20
So, the number of terms is 20.
Hope it helps you... ☺️✌️