Question

PLZ EXPLAIN AND I'LL GIVE BRAINLY!!!!

Answer 1

Hello there!

Given the sequence:

$\displaystyle \large{ 1, - 3,9, - 27,...}$

The question reveals it to be geometric sequence since it has common ratio.

Geometric Sequence / Ratio Formula

$\displaystyle \large{r = \frac{a_{n + 1}}{a_n} }$

Define 'r' as common ratio.

First, let's check the common ratio by using the formula above.

Ratio Check

$\displaystyle \large{r = \frac{ - 3}{1} \longrightarrow - 3 } \\ \displaystyle \large{r = \frac{ 9}{ - 3} \longrightarrow - 3 } \\ \displaystyle \large{r = \frac{ - 27}{9} \longrightarrow - 3 }$

Therefore, the common ratio or r-value is -3.

To find the 7th term of sequence, you can by using the General Geometric Terms.

General Term of Geometric

$\displaystyle \large{a_n = a_1 {r}^{n - 1} }$

a1 is defined as the first term of sequence.

r is common ratio.

n is the term.

Since we want to find 7th term:

• a1 = 1
• r = -3
• n = 7

$\displaystyle \large{a_7 =1{( - 3)}^{7 - 1} } \\ \displaystyle \large{a_7 =1{( - 3)}^{6} } \\ \displaystyle \large{a_7 =729 }$

Therefore, the 7th term of this sequence is 729.

Let me know if you have any questions!

Topic: Sequence and Series / Geometric Sequence