Find a formula for the sum of the first n terms of the sequence.1, 5, 9, 13,. ..Snn(4n- 3)XProve the validity of your formulaVerify the formula for n = 1.S1 1Assume that the formula is valid for n = k.(4k - 3) =S 15+ 9 13XThen,... + (4k - 3) + ak+ 1*= 1 59 + 13Sk+1Sk+ ak 1=ak1Use the equation for ak + 1and S to find the equation for Sk + 1Sk+ 1=Thus the formula is valid.Need Help?Read It

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Asked Oct 28, 2019
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I am very confused about this chapter and specifically on how the homework is breaking the problems down. 

Mathematical induction is just a proof involving replacements correct? 

 

Find a formula for the sum of the first n terms of the sequence.
1, 5, 9, 13,. ..
Snn(4n- 3)
X
Prove the validity of your formula
Verify the formula for n = 1.
S1 1
Assume that the formula is valid for n = k.
(4k - 3) =
S 15+ 9 13
X
Then,
... + (4k - 3) + ak+ 1*
= 1 59 + 13
Sk+1
Sk+ ak 1
=
ak1
Use the equation for ak + 1
and S to find the equation for Sk + 1
Sk+ 1
=
Thus the formula is valid.
Need Help?
Read It
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Find a formula for the sum of the first n terms of the sequence. 1, 5, 9, 13,. .. Snn(4n- 3) X Prove the validity of your formula Verify the formula for n = 1. S1 1 Assume that the formula is valid for n = k. (4k - 3) = S 15+ 9 13 X Then, ... + (4k - 3) + ak+ 1* = 1 59 + 13 Sk+1 Sk+ ak 1 = ak1 Use the equation for ak + 1 and S to find the equation for Sk + 1 Sk+ 1 = Thus the formula is valid. Need Help? Read It

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Expert Answer

Step 1

Given sequence is

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15,9,13.

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Step 2

The first term and the difference are

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d-aa n0,1, 2,3, ... d 5-1 d 4

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Step 3

The sum of n term ...

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n (24, +(n-1)d) 2

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