MyLab Test: Chapter 1Test This Question: 1 pt The first difference of a sequence

Question

MyLab Test: Chapter 1Test This Question: 1 pt The first difference of a sequence is 2, 5, 8, 11, 14, Find the first six terms of the original sequence in each of the following cas a. The first term of the original sequence is1 b. The sum of the first two terms in the original sequence is 12 c. The fifth term in the original sequence is 30 a. The first six terms are 1 Simplify your answers. Use ascending order) b. The first six terms are Simplify your answers. Use ascending order) c. The first six terms are Simplify your answers. Use ascending order ) Dard

Explanation / Answer

Let the series be : a,b,c,d,e,f,....

A) first term is 1 i.e. a=1

Therefore, as per given difference we will calculate rest terms:

b-a=2 => b= 2+a = 2+1 = 3

c-b =5 => c=5+b = 5+3 = 8

d-c=8 => d= 8+c = 8+8 =16

e-d = 11 =>e=11+d = 11+16 =27

f-e =14 =>f=14+e = 14 + 27 =41

B) here a+b=12

And ,. b-a = 2

Solving : we get b= 7 and a = 5

c-b = 5 => c = 5+b = 5 + 7 = 12

d-c = 8 => d = 8+c = 8+12 = 20

e-d =11 => e = 11+d = 11+ 20 = 31

f-e = 14 => f = 14+e = 14+31 = 45

C) e=5

f-e = 14 => f = 14 + e = 14 + 5 = 19

e-d = 11 => d = e-11 = 5- 11 = -6

d-c = 8 => c = d-8 = -6 -8 = -14

c-b = 5 => b = c-5 = -14-5 = -19

b-a = 2 => a = b-2 = -19-2 = -21

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