1.) Find the nth term of the sequence 1, 3, 7, 13, 21, 31… 2.) The three consecutive terms of an exponential sequence are the second,sixth and seventh terms of a linear sequence. Find the common ratio of the sequence.

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kenlingdad kenlingdad · Answer 1 · 2020-02-08T17:43:03+01:00

Answer:

1) xₙ = n² - (n - 1)

2) 1/4

Step-by-step explanation:

1) 1 = 1² - (1-1)

3 = 2² - (2-1)

7 = 3² - (3-1)

13 = 4² - (4-1)

...........

xₙ = n² - (n - 1)

2) three consecutive terms of an exponential sequence: x, rx , r²x

x: 2nd term of linear sequence

rx: 6th term of linear sequence rx = x + 4d

r²x: 7th term of linear sequence r²x = rx + d d = r²x - rx

rx = x + 4 * (r²x - rx) = x + 4r²x - 4rx

4xr² -5rx + x = 0

x(4r² -5r + 1) = 0

x (4r - 1) ( r - 1) = 0

x = 0 or r = 1/4 or r = 1

if either x = 0 or r = 1 d will be equals to "0" everything became 0

So the only reasonable answer is r = 1/4