How to find the 14th term of the sequence 8/9, -4/3, 2

Answer 1

Hello Tom!

Note that from 8/9 to -4/3 you multiply the first by -3/2 to get the second.

Let's test if this also applies to the second to the third.

-4/3*(-3/2) = 2 = 2 also applies!

We can assume that each therm is the previous times -3/2.

Therefore the 14th therm is

a₁₄ = a₁*(-3/2)¹³

a₁₄ = (8/9)*(-3/2)¹³

a₁₄ = 2³*(-3)^-2*(-3)¹³*2^-13 =2^-10*(-3)¹¹

Feel free to contact regarding any doubt in Math!

Answer 2

The ratio between the consecutive terms is constant --> sequence is geometric

(-4/3)(8/9) = -3/2

(2)(-4/3) = -3/2

the 14th term of the sequence is -172.9951172

Formula:

a_n = (a₁ * rⁿ) / r = (8/9 * (-3/2)ⁿ ) / (-3/2) = -16/27 * (-3/2)ⁿ = -16/27 * (-3/2)¹⁴ = -172.9951172

Answer 3

Hi Tom,

8/9, -4/3, 2 , ...

it is geometry sequence because( -4/3 )/ 8/9 = -3/2 and (2 ) / ( -4/3) = -3/2

a_{1 = 8/9} a_{2 = -4/3 n = 14 r = -3/2}

a_{14 =} a_{1 * r}¹³

 a_{14 = 8/9 ( -3/2) ^ 13 as you know the nth term of geometry sequence is} a_{n =} a_{1 *} r^n-1

I hope it is useful,

Minoo