Question

Write the explicit formula for the sequence. Then find the fifth term in the sequence.

Answer 1

Answer:

a) Explicit Formula : aₙ = 3. (-3)ⁿ⁻¹

b) Fifth term : a₅ = 243

Step-by-step explanation:

This sequence above is the Geometric sequence. The Geometric sequence is calculated using the formula

aₙ= a1.rⁿ⁻¹

where a1 = first term

r = common ratio

n = number of terms

From the above question, we are given

a1= 3, r=-3 and asked to find the explicit formula.

The explicit formula using the geometric sequence formula =

aₙ = 3. (-3)ⁿ⁻¹

b) The fifth term in the sequence is calculated as

aₙ = 3. (-3)ⁿ⁻¹

Where n = 5

a₅ = 3.(-3)⁵⁻¹

a₅ = 3.(-3)⁴

a₅= 243