How do u write a rule for th sequence to find the unknown term? 56.38, 51.28, 46.18, 41.08

The next term in sequence is 35.98

The rule for nth term of sequence is Where, n > 0 ( n =1, 2, 3, ....)

Solution:

Given sequence is:

56.38, 51.28, 46.18, 41.08

Let us first find the difference between the terms

Thus the difference between next term and previous term is same

Next term will be,

41.08 - 5.1 = 35.98

Thus the next term in sequence is 35.98

Therefore, the sequence is arithmetic sequence

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant

The formula for nth term of arithmetic sequence is given as:

Where,

= nᵗʰ term in the sequence

= the first term in the sequence

d = the common difference between terms

Here in this sequence

d = -5.1

Therefore,

Where, n > 0 ( n =1, 2, 3, ....)

Thus the rule to find nth term is found

sine

step-by-step explanation:

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.