Question

13. Find four numbers in AP such that their sum is 44 and the product of the second and the third
terms is 112.​

Answer 1

GIVEN:

• Sum of four terms in an AP = 44
• Product of the second and the third
• term is 112.

TO FIND:

• What are the four terms in an AP ?

SOLUTION:

Let the four terms of an AP be (a –3d), (a –d), (a + d), (a + 3d)

CASE:- 1)

✎ Sum of four terms in an AP is 44.

According to question:-

➙ (a –3d) + (a –d) + (a + d) + (a + 3d) = 44

➙ 4a = 44

➙ a = $\sf{\cancel\dfrac{44}{4}}$

❮ a = 11 ❯

CASE:- 2)

✎ Product of the second and the third term is 112.

According to question:-

➙ (a –d)(a + d) = 112

➙ a² +ad –ad –d² = 112

➙ a² –d² = 112....1)

Put the value of a in equation 1)

➙ (11)² –d² = 112

➙ 121 –d² = 112

➙ –d² = 112 –121

➙ –d² = –9

➙ d² = 9

➙ d = $\sf{\sqrt{9}}$

❮ d = 3 ❯

Four numbers in AP:-

✦ (a –d) = (11 –3) = 8

✦ (a + d) = (11 + 3) = 14

✦ (a –3d) = [11 –3(3)] = 11 –9 = 2

✦ (a + 3d) = [11 + 3(3)] = 11 + 9 = 20

❝ Hence, the four numbers of an AP are 8, 14, 2 and 20 ❞

______________________

Answer 2

Qᴜᴇsᴛɪᴏɴ :

➥ Find four numbers in AP such that their sum is 44 and the product of the second and the third

terms is 112.

Aɴsᴡᴇʀ :

➥ The fours numbers in AP = 2, 8, 14, 20

Gɪᴠᴇɴ :

➤ The Sum of four terms in AP = 44

➤ Product of the second and the third term = 112

Tᴏ Fɪɴᴅ :

➤ The four terms in AP = ?

Sᴏʟᴜᴛɪᴏɴ :

Four numbers in AP are

a - 3d, a - d, a + d, a + 3d

Their sum is 44

➺ (a - 3d) + (a - d) + (a + d) + (a + 3d) = 44

➺ 4a = 44

➺ a = 44/4 $\:$

➺ a = 11

Product of the 2nd and the 3rd term is 112

➺ (a - d)(a + d) = 112

➺ a² - d² = 112

➺ 11² - d² = 112

➺ 121 - d² = 112

➺ d² = 121 - 112

➺ d² = -9

➺ d = √9

➺ d = 3

If a = 11, d =3, then the four numbers are

⪼ a - 3d = 11 - 3 × 3 = 11 - 9 = 2

⪼ a - d = 11 - 3 = 8

⪼ a + 3d = 11 + 3 = 14

⪼ a + 3d = 11 + 3 × 3 = 20

Hence, the four numbre in AP are 2, 8, 14, 20.