SOLUTION: Consider each given sequence start. i) Classify each as arithmetic, geometric, and/or none of these. ii) Find the 28th term. iii) Find the sum of the first 7 terms, call it S7

Question 1178152: Consider each given sequence start. i) Classify each as arithmetic, geometric, and/or none of these. ii) Find the 28th term. iii) Find the sum of the first 7 terms, call it S7 .

a) 44, −6, 44, −4,

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
,, , ,...
1st term
2nd term
3rd term
=> no common difference is

=> no common ratio
i) Classify each as arithmetic, geometric, and/or none of these.
=> no common difference , no common ratio
so, the sequence is neither arithmetic nor geometric
to find th term formula use differences:
........................

.........................................................................
.................................................................
......................................................=>rd difference, so th term formula
will be rd degree function

plug in some of the values from the sequence, and then solving the resulting system of equations

.......->first term, so

........eq.1
.......->first term, so

............eq.2

........eq.3

............eq.4

subtract eq.1 from eq.2

.............eq.3
subtract eq.1 from eq.3 (reason: next term is again)

.......solve for

.............eq.4

go to
........eq.3...., substitute
......solve for

.......................eq.5
go to

.............eq.4, substitute

.................eq.6

subtract eq.1 from eq.4
............substitute from eq.6 and from eq.5

....solve for

go to
.................substitute

go to
........................substitute

go to
........eq.1substitute ,, and

so, coefficients are:
, , ,

and equation is:

ii) Find the th term.

iii) Find the sum of the first terms, call it .
we have ,, , ,...
first find th, th, and th term

,, , ,,,

the sum is

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