How many terms will it take to get the sum 1046.5 in AP 7, 10⩾,14,...
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Answered by
9
Answer:
first term of AP=a=7
common difference =10
2
1
−7=3
2
1
Sum of AP of n terms is
2
n
[2a+(n−1)d]
so
2
n
[2a+(n−1)d]=1046.5
⇒
2
n
[2×7+(n−1)3.5]=1046.5
⇒14n+3.5n
2
−3.5n=1046.5×2
⇒3,5n
2
+10,5n=2093
⇒n
2
+3n−598=0
⇒n
2
+26n−23n−598=0
⇒n(n+26)−23(n+26)=0
⇒(n−23)(n+26)=0
⇒n=23
as n is a positive number
so number of terms is 23
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Answered by
1
Answer:
A
23
first term of AP=a=7
common difference =10
2
1
−7=3
2
1
Sum of AP of n terms is
2
n
[2a+(n−1)d]
so
2
n
[2a+(n−1)d]=1046.5
⇒
2
n
[2×7+(n−1)3.5]=1046.5
⇒14n+3.5n
2
−3.5n=1046.5×2
⇒3,5n
2
+10,5n=2093
⇒n
2
+3n−598=0
⇒n
2
+26n−23n−598=0
⇒n(n+26)−23(n+26)=0
⇒(n−23)(n+26)=0
⇒n=23
as n is a positive number
so number of terms is 23
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