The common ratio, r, in a geometric sequence whose second term is
24 and whose fifth term is 1536

r = 4

Step-by-step explanation:

The general term of the geometric sequence is ⇒ an = a * rⁿ⁻¹

Where a is the first term and r is the common ratio

The second term is 24 ⇒ 24 = a * r²⁻¹ = a r   ⇒(1)

The fifth term is 1536   ⇒ 1536 = a * r⁵⁻¹ = a r⁴ = (a r) * r³  ⇒ (2)

By substitution with the value of (a r) from eq.(1) at eq.(2)

So, 1536 = 24 r³

∴ r³ = 1536/24 = 64

∴ r = ∛64 = 4

so, the common ratio r = 4

And the first term = 24/4 = 6

The geometric sequence will be ⇒ an = 6 * 4ⁿ⁻¹

one that is bigger than 3 1/2

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116