Question

Find the 100 th and the nth term for each of the following sequences. a. 1,3,5,7,… b. 70,130,190,… c. 1,4,16,… d. 5,5 3

,5 5
,5 7
,… e. 106+7⋅3 27
,106+8⋅3 27
,106+9⋅3 27
,…

Answer 1

Hi,

We can imagine that a space mean power.

Explanation:

`1)\\1,3,5,7,...\\1,1+2*1,1+2*2,1+2*3,...,1+2*99,...,1+2*(n-1)\\u_(100)=1+2*(100-1)=199\\u_(n)=1+2*(n-1)=2n-1\\`

2)

`70,130,190,...\\70,70+1*60,70+2*60,...,70+99*60,...,70+(n-1)*60\\u_(100)=70+99*60=6010\\u_(n)=70+(n-1)*60=10+60n\\`

3)

`1,4,16,...\\1, (2^2)^1, (2^2)^2,(2^2)^3,...,(2^2)^(99), (2^2)^(n-1)\\\\u_(100)=4^(99)\\u_(n)=4^(n-1)\\\\`

4)

`5,5^3,5^5,5^7,...\\5^(1+0*2),5^(1+1*2),5^(1+2*2),5^(1+3*2),...,5^(1+99*2),...,5^(1+(n-1)*2)\\\\u_(100)=5^(1+99*2)=5^(199)\\\\u_(n)=5^(1+(n-1)*2)=5^(2n-1)\\`

5)

`106+7*3^(27), 106+8*3^(27),106+9*3^(27),...\\\\106+(0+7)*3^(27), 106+(1+7)*3^(27),106+(2+7)*3^(27),...,106+((100-1)+7)*3^(27),...106+((n-1)+7)*3^(27)\\\\u_(100)=((100-1)+7)*3^(27)=106*3^(27)\\\\u_(n)=106+((n-1)+7)*3^(27)=106+(n+6)*3^(27)\\`