Which shows a recursive and an explicit formula for a sequence whose initial term is 14 and whose common difference is −4? A. A(1) = 14; A(n) = (n − 1) −4; A(n) = 14 + (n − 1)(−4) B. A(1) = 14; A(n) = (n + 1) −4; A(n) = 14 + (n − 1)(−4) C. A(1) = 14; A(n) = (n − 1) − 14; A(n) = 14 + (n − 1)(−14) D. A(1) = 14; A(n) = (n + 1) − 14; A(n) = 14 + (n + 1)(14)

A. A(1) = 14; A(n) = (n − 1) −4; A(n) = 14 + (n − 1)(−4)

Step-by-step explanation:

Arithmetic sequence is a sequence that is identified by their common difference. Let a be the first term, n be the number of terms and d be the common difference.

For an arithmetic sequence, common difference 'd' is added to the preceding term to get its succeeding term. For example if a is the first term of a sequence, second term will be a+d, third term will give a+d+d and so on to generate sequence of the form,

a, a+d, a+3d, a+4d...

Notice that each new term keep increasing by a common difference 'd'

The nth term of the sequence Tn will therefore give Tn = a+(n-1)d

If the initial (first) term is 14 and common difference is -4, the nth of the sequence will be gotten by substituting a = 14 and d = -4 in the general formula to give;

Tn = 14+(n-1)-4 (which gives the required answer)

Tn = 14-4n+4

Tn = 18-4n

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.