The third term of an arithmetic sequence is 21,and the eighth term is 56. the first term is?

This is the concept of sequences and series
the nth term of the arithmetic sequence is given by:
nth=ar^(n-1)
where;
a=first term
r=common ratio
n=th number of terms;
thus;
21=ar^(3-1)
21=ar^2i
the eighth term will be:
56=ar^(8-1)
56=ar^7ii
thus from i
a=21/r^2
from ii
a=56/r^7
hence combining i and ii we get:
21/r^2=56/r^7
multiplying through by a^7 we get:
21r^5=56
dividing both sides by 21 we get:
r^5=8/3
hence;
r=(8/3)^(1/5)=1.22
thus, the value of a will be:
a=21/r^2
a=21/(1.22)^2
a=14.185
the first term is 14.185

Yes. there is a constant ratio of number of calories to gram of protein.12/3=24/4=32/8=44/11=4