find the sum of all the multiples of 7 between 100 and 200
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Answer: 105 , 112 , 119 , 126 , 133 , 140 , 147 , 154 , 161 , 168 , 175 , 182 , 189 , 196 .
Answer: 105 , 112 , 119 , 126 , 133 , 140 , 147 , 154 , 161 , 168 , 175 , 182 , 189 , 196 .therefore total multiples of 7 b/w 100 & 200 are :- 14 .
Answered by
0
Answer:
Multiples of 7 between 100 and 200 :
105 , ...... , 196
First term = a = 105
d = 7
a_n=a+(n-1)d
196=105+(n-1)(7)
196-105=(n-1)(7)
\begin{gathered}\frac{196-105}{7}=n-1 \\\frac{196-105}{7}+1=n\end{gathered}
7
196−105
=n−1
7
196−105
+1=n
14 = n
Sum of multiples of 7 between 100and 200 :
\begin{gathered}S_n=\frac{n}{2}(a+a_n) \\S_{14}=\frac{14}{2}(105+96) \\S_{14}=1407\end{gathered}
S
n
=
2
n
(a+a
n
)
S
14
=
2
14
(105+96)
S
14
=1407
Hence The sum of multiples of 7 between 100 and 200 is 1407
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