How many terms of the A.P 5,7,9.....have to be added to get the sum 320
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11th
Maths
Sequences and Series
Arithmetic Progression
How many terms of the A.P, ...
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Asked on December 20, 2019 by
Aamir Spoorthi
How many terms of the A.P,3,5,7,9,−−−−− must be added to get the sum of 120?
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ANSWER
120=
2
n
[a+a+(n−1)d]
where n= no of terms
a=first term
d=common difference
120=
2
n
[3+3+(n−1)2]
240=n[3+3+(n−1)2]
240=n[6+2n−2]
240=n[4+2n]
n
2
+2n−120=0
n
2
+12n−10n−120=0
n(n+12)−10(n+12)=0
(n−10)(n+12)=0
n=10
no of terms must be added 10−4=6 terms
Answer:
16
Step-by-step explanation:
a=5
d=2
Sn=320
Sn=n/2(2a+(n-1)d)
320= n/2(2×5+(n-1)2)
320=n/2(10+2n-2)
320=n/2(8+2n)
320×2=n(8+2n)
640=8n+2n²
8n+2n²-640=0
2(n²+4n-320)=0
n²+4n-320=0
n²+20n-16n-320
n(n+20)-16(n+20)
(n-16)(n+20)
n=16,-20(Not possible)
so,the answer is 16