Question

Four numbers are in A.P. The sum of first and fourth terms is 14 and the product of second and third is 45 find the numbers.
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Answer 1

Answer:

1,5,9,13

Step-by-step explanation:

1+13=14

5x9=45

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Answer 2

EXPLANATION.

Four number are in ap.

The sum of first and fourth term = 14

Products of second and third = 45

To find the number.

According to the question,

Case = 1.

Let the four terms in ap

=> a - 3d , a - d, a + d, a + 3d

=> The sum of first and four term = 14

=> a - 3d + ( a + 3d ) = 14

=> a - 3d + a + 3d = 14

=> 2a = 14

=> a = 7

Case = 2.

products of second and third = 45

=> ( a - d) ( a + d) = 45

=> a² - d² = 45

=> (7)² - d² = 45

=> 49 - d² = 45

=> -d² = -4

=> d² = 4

=> d = 2

Therefore,

First term = a = 7

second term = a + d = 7 + 2 = 9

third term = a + 2d = 7 + 2(2) = 11

fourth term = a + 3d = 7 + 3(2) = 13

Sequence = 7 , 9 , 11 , 13 ......