13. If 12 + 22 + 32 + + ........ + 5122 = m, then
22 +42 +62 + ........ + 10242 is equal to
(a) 3m
(b) 4m
(c) m2
(d) m3
Answers
Answer:
Airthmetic equation is given by
a_{n} = a_{1}+(n-1)d
S_{n} = \frac{n}{2}[a_{1}+a_{n}]
d = a_{2}-a_{1}
Where a_{n} is the nth term , a_{1} is the first term and d is the common difference .
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pradhansaditya4653
24.03.2018
Math
Secondary School
+13 pts
Answered
Given that (12+22+32+.......102)=385 ,then the value of (22+42+62+.......+202) is
2
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jainsamarth
jainsamarth Ambitious
The answer is 750 ... please reply.
3.5
6 votes
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JackelineCasarez Ambitious
Answer:
The value of (22+42+62+.......+202) is 1120 .
Step-by-step explanation:
Airthmetic equation is given by
a_{n} = a_{1}+(n-1)d
S_{n} = \frac{n}{2}[a_{1}+a_{n}]
d = a_{2}-a_{1}
Where a_{n} is the nth term , a_{1} is the first term and d is the common difference .
As given the equation
12 + 22 + 32 + .......102 = 385
Now consider the series 22 + 42 + 62 + ....... + 202 .
a_{1}=22
a_{2} = 42
d =42-22
d = 20
a_{n}=202
202=22+(n-1)20
202 = 22 + 20n - 20
202 = 2 + 20n
202 - 2 = 20n
200 = 20n
n = \frac{200}{20}
n = 10
Thus the series 22 + 42 + 62 + ....... + 202 contains 10 terms .
S_{10} = \frac{10}{2}[22+202]
S_{10} = \frac{10}{2}\times [224]
S_{10} =5\times [224]
S_{10} =1120
Therefore the value of (22+42+62+.......+202) is 1120 .
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