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

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter12: Sequences, Series And Binomial Theorem
Section12.2: Arithmetic Sequences
Problem 12.34TI: Find the first term and common difference of a sequence where the third term is 2 and the twelfth...
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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
Transcribed Image Text: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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