Question

the sum of the 4th and 8th term of AP is 24 and the sum of 6th and 10th term is 44 find the first three terms of AP ​

Answer 1

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Answer 2

$\underline{\underline\textbf{Given...}}$

✮ a4 + a8 = 24

✮ a6 + a10 = 44

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀

$\underline{\underline\textbf{To\:find...}}$

✮ The first three terms of Ap...

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

$\underline{\underline\textbf{Solution...}}$

✰✰ We know that...

a + 3d = a4

a + 7d = a8

a + 5d = a6

a + 9d = a10

✰✰ Now...

a + 3d + a + 7d = 24 _________ eq 1...

---➣ 2a + 10d = 24 ________ eq 2...

a + 5d + a + 9d = 44 _________ eq 3...

---➣ 2a + 14d = 44 ________ eq 4...

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

✰✰ From equation 2 & equation 4...

⠀⠀⠀⠀ ⠀⠀2a + 10d = 24 ________ eq 2...

⠀⠀⠀ ⠀⠀ 2a + 14d = 44 ________ eq 4...

⠀⠀⠀⠀ ⠀ ⠀-⠀ -⠀⠀⠀⠀-

⠀⠀⠀⠀ ⠀______________

⠀⠀ ⠀⠀⠀⠀ ⠀ ⠀-4d = - 20

⠀ ⠀⠀⠀⠀⠀⠀⠀ ⠀4d = 20

⠀⠀ ⠀⠀⠀⠀⠀⠀ ⠀ d = 20 / 4

• ⠀⠀ ⠀⠀⠀⠀$\boxed{\sf{\red{\:d\:=\:4}}}$ ⠀ ⠀

⠀ ⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

✰✰ Substituting value of d in equation 2...to find the value of a...

---➣ 2a + 10d = 24 ________ eq 2...⠀

---➣ 2a + 10(5) = 24

---➣ 2a + 50 = 24

---➣ 2a = 24 - 50

---➣ 2a = 26

---➣ a = 26 / 2

• $\boxed{\sf{\red{\:a\:=\:13}}}$

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

✰✰ Now we have both the value of a and the value of b...

Since, we know the general form of Ap...

a, a + d, a + 2d

13, 13 + 5, 13 + 2 × 5

• $\boxed{\sf{\red{\:13,\:18,\:23}}}$