Shinihai10idn
Answered

Suriin ang IDNStudy.com at makakuha ng mga sagot sa iyong mga tanong sa iba't ibang paksa. Magtanong ng anumang bagay at makatanggap ng agarang tugon mula sa aming dedikadong komunidad ng mga eksperto.

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.

Maraming salamat sa iyong pakikilahok. Patuloy na magbahagi ng iyong mga ideya at kasagutan. Ang iyong kaalaman ay mahalaga sa ating komunidad. Gawin mong pangunahing mapagkukunan ang IDNStudy.com para sa maasahang mga sagot. Nandito kami para sa iyo.