Find the 6th term of the geometric sequence, given the first term and common ratio a1= 5 and r=3/2

Answer

37.96875

Explanation

In geometric sequence we use the formula below to find the nth of a sequence.

Tn = ar⁽ⁿ⁻¹⁾

Where a ⇒ first term

n ⇒ the term we are looking for

T₆ = 5 × (3/2)⁶⁻¹

= 5 × (3/2)⁵

= 5 × 243/32

= 1215/32

= 37 31/32

= 37.96875

i believe the answer is d.

hope it you! : d

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.