Question

Find the 14th term of the geometric sequence 7,28,112

Answer 1

Solution:

We are to find the 14th term in the G.P sequence: 7, 28, 112.........n

1st term (a)$= 7$

Common ratio:$\frac{28}{7} = 4$

Formula for finding the nth term of a G.P: $tn = a {r}^{n - 1}$

Where: t = term, n = the given number of term, a = the 1st term, and r = the common ratio.

Replacing for the values of the variables in the above formula.

$t14 = 7 \times {4}^{14 - 1}$

$t14 = 7 \times {4}^{13}$

$t14 = 7 \times 67108864$

$t14 = 469762048$

Therefore: the 14th term = 469762048

I hope this helps.

Answer 2

Answer: 469762048

Step-by-step explanation:

1: 7*4^0=

7*1=7

2:7*4^1=

7*4=28

3: 7*4^(3-1)=

7*4^2=

7*16=112

14: 7*4^(14-1)=

7*4^13=469762048