Answer:
Next term of the sequence is 8/5.
Step-by-step explanation:
The given sequence is 25, 10, 4, .........
We have to tell the next term of the sequence or 4th term of the sequence.
First we will identify the sequence whether it is arithmetic or geometric.
For arithmetic sequence common difference should be same.
10 - 25 = -15
4 - 10 = -6
Therefore this sequence is not arithmetic.
Now for geometric sequence there should be a common difference in each term.
10/25 = 2/5
4/10 = 2/5
Therefore the sequence is geometric
Now we know the explicit formula of a geometric formula is
[tex]T_{n}=ar^{n-1}[/tex]
here a = 25
r = 2/5
and number of term n = 4
[tex]T_{4}=25(\frac{2}{5})^{4-1}=25(\frac{2}{5})^{3}[/tex]
Therefore T4 = 25×(2×2×2)/5×5×5 = (25×8)/125 = 8/5 ≈ 1.6
