Final answer:
The 35th term in the geometric sequence 7, 7/5, 7/25, ... is approximately 0.00000000245.
Step-by-step explanation:
The 35th term in the geometric sequence 7, 7/5, 7/25, ... can be found using the formula:
an = a1 · r(n-1)
Where a1 is the first term (7) and r is the common ratio (1/5).
Plug in the values to find the 35th term:
a35 = 7 · (1/5)(35-1)
Calculate the exponent first: (1/5)34. Use a calculator or simplify to get the result:
(1/5)34 = 1/285,311,670,611, or approximately 3.50 × 10-9
Now, plug in the result into the formula and simplify:
a35 = 7 · (1/285,311,670,611)
= 7/285,311,670,611, or approximately 0.00000000245