Question

What is the 6th term in this sequence? 1, 3, 9, 27, . . .

Answer 1

a₆ = 243

Explanation:

there is a common ratio between consecutive terms , that is

3 ÷ 1 = 9 ÷ 3 = 27 ÷ 9 = 3

this indicates the sequence is geometric with nth term

`a_(n)` = a₁ ×
`r^(n-1)`

where a₁ is the first term and r the common ratio

here a₁ = 1 and r = 3 , then

a₆ = 1 ×
`3^(5)` = 243

Answer 2

243

Solution:

• We have a geometric sequence here, meaning that we use multiplication/division in order to get to the next term.
• In this case, we multiply each term by 3.
• 1 times 3 is 3, 3 times 3 is 9, 9 times 3 is 27...
• In order to find the sixth term, we should take the fifth term and multiply it by 3.
• In order to find the fifth term, we need to take the fourth term and multiply it by 3.
• Multiply:
• 81
• So the fifth term of this sequence is 81.
• Now, multiply 81 times 3:
• 243
• Therefore, the sixth term in this sequence is equal to 243.

Hope it helps.

Do comment if you have any query.