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^2.....i
the eighth term will be:
56=ar^(8-1)
56=ar^7.......ii
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
