Question

that the fourth number is 7 times the first number
45) If four numbers in arithmetic progression are such
and their sum is 64, then the numbers are:
A. 3,6,9,12
B. 4,10,16,22
C. 5,10,15,20
D. 4,12,20,28​

Answer 1

Correct Question:

If four numbers in arithmetic progression are such that the fourth number is 7 times the first number and their sum is 64, then the numbers are:

A. 3,6,9,12

B. 4,10,16,22

C. 5,10,15,20

D. 4,12,20,28

Given:

✰ Four numbers in arithmetic progression.

✰ The fourth number is 7 times the first number.

✰ The sum of four numbers = 64

To find:

✠ The numbers

Solution:

Let the numbers be a, a + d, a + 2d, a + 3d

Given that the fourth number is 7 times the first number,

➤ a + 3d = 7a

➤ 3d = 7a - a

➤ 3d = 6a

➤ d = 6a/3

➤ d = 2a

Now,

⇾The sum of four numbers = 64

⇾a + a + d + a + 2d + a + 3d = 64

Put the values of d in,

⟹ a + a + 2a + a + 2 ( 2a ) + a + 3 (2a ) = 64

⟹ a + a + 2a + a + 2 × 2a + a + 3 × 2a = 64

⟹ a + a + 2a + a + 4a + a + 6a = 64

⟹ 4a + 2a + 4a + 6a = 64

⟹ 16a = 64

⟹ a = 64/16

⟹ a = 4

Now, find out d,

⇾ d = 2a

⇾ d = 2 × 4

⇾ d = 8

Find the numbers,

➣ a = 4

∴ The first number = 4

➣ a + d

➣ 4 + 8

➣ 12

∴ The second number = 12

➣ a + 2d

➣ 4 + 2 × 8

➣ 4 + 16

➣ 20

∴ The third number = 20

➣ a + 3d

➣ 4 + 3 × 8

➣ 4 + 24

➣ 28

∴ The forth number = 28

Hence,

Option D. 4,12,20,28 is correct ✔

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