The third term of an arithmetic progression is 6 while the sum of the first twelve terms is 282. find the common difference and the first term

d = 5 and a₁ = - 4

Step-by-step explanation:

The n th term of an arithmetic sequence is

= a₁ + (n - 1)d

Given a₃ = 6, then

a₁ + 2d = 6 → (1)

The sum to n terms of an arithmetic sequence is

= [ 2a₁ + (n - 1)d ]

Given = 282, then

6 [ 2a₁ + 11d ] = 282 ( divide both sides by 6 )

2a₁ + 11d = 47 → (2)

We can now solve (1) and (2) for d and a₁

Multiply (1) by - 2

- 2a₁ - 4d = - 12 → (3)

Add (2) and (3) term by term

7d = 35 ( divide both sides by 7 )

d = 5

Substitute d = 5 in (1) and solve for a₁

a₁ + 10 = 6 ( subtract 10 from both sides )

a₁ = - 4

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.  

87%

step-by-step explanation:

apex answer