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1. Find a formula for the sum: 2+ 6+ 10 ... + 2(2n - 1)

Question
1. Find a formula for the sum: 2+ 6+ 10 ... + 2(2n - 1)
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1. Find a formula for the sum: 2+ 6+ 10 ... + 2(2n - 1)

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Step 1

The given sequence is 2+6+10+... +2(2n–1).

Step 2
Consider the given sequence that is 2+6+10+... +2(2n-1)
Observe that the above sequence is in the form of the Arithmetic progression
Let s represents the sum of the n terms
Then the sum of n terms in Arithmetic progression is given by S 2a(
2 L
d
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Consider the given sequence that is 2+6+10+... +2(2n-1) Observe that the above sequence is in the form of the Arithmetic progression Let s represents the sum of the n terms Then the sum of n terms in Arithmetic progression is given by S 2a( 2 L d

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Step 3
The given sequence is 2 6 10..2(2n -1)
Take 2 as common and solve as follows.
S 2[1+3+5.. (2n-1)]
n
= 2
2
(2x1+(-1)2)
(a 1,d= 2)
= 2(2+ 2n
21-2)
n
= 2
2
(2n
S 2n2
Thus, the sum of 2 +6+10 +...2(2n-1) is 2n2
help_outline

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The given sequence is 2 6 10..2(2n -1) Take 2 as common and solve as follows. S 2[1+3+5.. (2n-1)] n = 2 2 (2x1+(-1)2) (a 1,d= 2) = 2(2+ 2n 21-2) n = 2 2 (2n S 2n2 Thus, the sum of 2 +6+10 +...2(2n-1) is 2n2

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