Question

4. Find the 7th term of geometric sequence: 5, 10, 20 ...
a.260
b.264
c.320
d.324
5. Find the 8th term of geometric sequence: 4, 20, 100 ... *
a.78,125
b.278, 125
c.312, 500
d.315 500

Answer 1

Answer:

4.c.320 is the correct option.

5.c 312,500 is the correct option

Step-by-step explanation:

4)sol

R = a2 /a1 = 10/5 = 2R

an = a1 × r ×n-1, where a1 = first term and r = common ratio = a2/a1)

5 × 2^n-1 = 5 × 2^7-1 = 5 × 2⁶ = 5 × 64 = 320

5). Given : a1 = 4 , a2 = 20 ,a3 = 100,.

n = 8

r = a2/a1 = 20/4 = 5

Here,a8 = a1 × r ^n-1 = 4 × 5^8-1 = 4 × 5⁷

a8 = 4× 78,125 = 312,500.

Hope it helps ☺️

Answer 2

Given:

1. geometric sequence: 5, 10, 20 ...

2. geometric sequence: 4, 20, 100 ...

To find:

1. 7th term

2.  8th term

Solution:

we know the formula for the nth term in geometric progression is:

$a_{n}$ = a$r^{n-1}$, where a is the first term and r is the common ratio.

now,

1. The common ratio for the sequence 5, 10, 20... is 2.

so,

$a_{7}$ = 5 × $2^{7-1}$

$a_{7}$ = 5 × $2^{6}$

$a_{7}$ = 5 × 64

$a_{7}$ = 320

Hence the 7th term is 320

therefore the answer is c.

2. The common ratio for the sequence 4, 20, 100... is 5.

so,

$a_{8}$ = 4 × $5^{8-1}$

$a_{8}$ = 4 × $5^{7}$

$a_{8}$ = 4 × 78125

$a_{8}$ = 312500

hence the 8th term is 312500

therefore the answer is c