Shinihai10idn
Answered

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Create a sequence satisfying the ff: prove that it satisfies the given conditions.
1. The first term is 12.
2. The third term is 1/2.​

Sagot :

Wynliviaidn

Answer and step-by-step explanation:

To create the sequence, let's find the common difference to find the missing term which is the second term.

Use the formula for an arithmetic sequence:

An = A1 + (n - 1)d

where

An is the nth term,

A1 is the first term,

n is the number of terms, and

d is the common difference.

Let's substitute the given values to the formula. Then simplify.

An = A3 = 1/2

A1 = 12

n = 3

1/2 = 12 + (3 - 1)d

1/2 = 12 + 2d

1/2 - 12 = 2d

-23/2 = 2d

-23/2 /2 = 2d/2

-23/4 = d

Thus, the common difference is -23/4.

Let's find the second term of the sequence by subtituting the formulas again. Then simplify.

A2 = 12 + (2 - 1)(-23/4)

A2 = 12 + (1)(-23/4)

A2 = 12 + (-23/4)

A2 = 25/4

Therefore, the sequence is 12, 25/4, 1/2.

Proof:

Check if the given third term will be the same after you add the common difference to the second term.

A2 + d = A3

25/4 + (-23/4) = 1/2

1/2 = 1/2

Therefore, it satisfies the given conditions and the sequence is correct.