Question

8;18;30;44;.... calculate the nth term of the sequence

Answer 1

Hello,

a(1)=8
a(2)=18=8+10=8+8+2=2*8+2=2*8+2*(2-1)
a(3)=30=18+12=2*8+2*(2-1)+8+2*(3-1)=3*8+2(1+2)
a(4)=44=a(3)+14=3*8+2(1+2)+8+2(4-1)=4*8+2(1+2+3)....

a(n)=n*8+2(1+2+3+...+(n-1))
= 8n+2*n*(n-1)/2)=8n+n(n-1)=n²+7n

$\boxed{a_{n}= n^2+7n}$

n=1=>1²+7*1=8
n=2=>2²+7*2=4+14=18
n=3=>3²+7*3=9+21=30
n=4=>4²+7*4=16+28=44
...

Answer 2

The nth term of the sequence will be Tn = n^2 + 7n

How to calculate the nth term of a sequence

Given the sequence of numbers expressed as:

8;18;30;44;

Their common difference will form an A P as shown:

10, 12, 14...

Next term  = preceding term  + 2

Next term = 14 + 2

Next term = 16

The next term of the squence will be 44 + 16 = 60

The nth term of the sequence will be Tn = n^2 + 7n

Learn more on nth term here: https://brainly.com/question/7882626