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

a1 = 3, r=-3

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