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^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