Answered

IDNStudy.com, ang komunidad ng pagbabahagi ng kaalaman at mga sagot. Makakuha ng impormasyon mula sa aming mga eksperto, na nagbibigay ng detalyadong sagot sa lahat ng iyong mga tanong.

the 4th term of an arithmetic sequence is -1 and the 6th term is 9. write the first five terms of the sequence​

Sagot :

AiTakiidn

Step-by-step explanation:

To find the first five terms of an arithmetic sequence, we need to determine the common difference \( d \) and the first term \( a_1 \). We know the 4th term (\( a_4 \)) is -1 and the 6th term (\( a_6 \)) is 9.

In an arithmetic sequence, the \( n \)-th term is given by:

\[ a_n = a_1 + (n - 1)d \]

Using the information provided:

1. For the 4th term: \( a_4 = a_1 + 3d = -1 \)

2. For the 6th term: \( a_6 = a_1 + 5d = 9 \)

Now, we can solve these two equations to find \( a_1 \) and \( d \):

**Step 1:** Subtract the first equation from the second to find \( d \):

\[ (a_1 + 5d) - (a_1 + 3d) = 9 - (-1) \]

\[ 2d = 10 \]

\[ d = 5 \]

**Step 2:** Substitute \( d \) back into the first equation to find \( a_1 \):

\[ a_1 + 3(5) = -1 \]

\[ a_1 + 15 = -1 \]

\[ a_1 = -1 - 15 \]

\[ a_1 = -16 \]

Now, we have the first term \( a_1 = -16 \) and the common difference \( d = 5 \). Let's find the first five terms:

1. **First term (\( a_1 \))**: \(-16\)

2. **Second term (\( a_2 \))**: \( a_1 + d = -16 + 5 = -11 \)

3. **Third term (\( a_3 \))**: \( a_1 + 2d = -16 + 10 = -6 \)

4. **Fourth term (\( a_4 \))**: \( a_1 + 3d = -16 + 15 = -1 \)

5. **Fifth term (\( a_5 \))**: \( a_1 + 4d = -16 + 20 = 4 \)

So, the first five terms of the sequence are: \(-16, -11, -6, -1, 4\).

Ang iyong kontribusyon ay napakahalaga sa amin. Huwag kalimutang bumalik upang magtanong at matuto ng mga bagong bagay. Sama-sama tayong lumikha ng isang mas matibay na samahan. May mga katanungan ka? Ang IDNStudy.com ang may sagot. Salamat sa iyong pagbisita at sa muling pagkikita.