Respuesta :
Answer: 81,920
Step-by-step explanation:
10 (1st)
10 * 2 = 20 (2nd)
20 * 2 = 40 (3rd)
40 * 2 = 80 (4th)
80 * 2 = 160 (5th)
160 * 2 = 320 (6th)
320 * 2 = 640 (7th)
640 * 2 = 1,280 (8th)
1,280 * 2 = 2,560 (9th)
2,560 * 2 = 5,120 (10th)
5,120 * 2 = 10,240 (11th)
10,240 * 2 = 20,480 (12th)
20,480 * 2 = 40,960 (13th)
40,960 * 2 = 81,920 (14th)
The 14th term of the geometric sequence 10, 20, 40, ... is 81920.
What is geometric sequence?
"A geometric sequence is a special type of sequence. It is a sequence in which every term (except the first term) is multiplied by a constant number to get its next term."
The geometric sequence formulas include the formulas for finding its nth term and the sum of its n terms. We will see the geometric sequence formulas related to a geometric sequence with its first term 'a' and common ratio 'r' (i.e., the geometric sequence is of form [tex]a, ar, ar^{2},ar^{3} ,.............[/tex]). Here are the geometric sequence formulas.
[tex]a_{n}=ar^{n-1}[/tex]
Given geometric sequence
10, 20, 40, .........
From the given sequence
[tex]a_{1} = 10[/tex], [tex]a_{2} = 20[/tex], [tex]a_{3} = 40[/tex]
Using the formula [tex]a_{n}=ar^{n-1}[/tex]
⇒ [tex]a_{4} = 10(2)^{3} =80[/tex]
⇒ [tex]a_{5} = 10(2)^{4} =160[/tex]
⇒ [tex]a_{6} = 10(2)^{5} =320[/tex]
⇒ [tex]a_{7} = 10(2)^{6} =640[/tex]
⇒ [tex]a_{8} = 10(2)^{7} =1280[/tex]
⇒ [tex]a_{9} = 10(2)^{8} =2560[/tex]
.
.
.
⇒ [tex]a_{14} = 10(2)^{13} =81920[/tex]
Hence, the 14th term of the geometric sequence 10, 20, 40, ... is 81920.
Learn more about geometric sequence here
https://brainly.com/question/11266123
#SPJ2
