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

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



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
...

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Hello! i hope this
since the cosine is the ratio of the adjacent side to the hypotenuse, you can see that cos 60° = ½. answer. according to the property of cofunctions (topic 3), sin 30° is equal to cos 60°. sin 30° = ½.