Question

find the four numbers in AP such that the sum of 2nd and 3rd terms is 22 and product of first and fourth terms is 85 ​

Answer 1

Step-by-step explanation:

Suppose 4 no. in AP are:-

( a - 3d ) , ( a - d ) , ( a + d ) , ( a + 3d )

• Sum of 2nd and 3rd terms is 22

• ( a - d ) + ( a + d ) = 22

• a - d + a + d = 22

• 2( a ) = 22

• a = 11

• Product of 1st and 4th terms is 85

• ( a - 3d ) ( a + 3d ) = 85

• ( 11 - 3d ) ( 11 + 3d ) = 85

• 121 - 9 ( d )^2 = 85

• 121 - 85 = 9 ( d )^2

• 36 = 9 ( d )^2

• 4 = ( d )^2

• +/- 2 = d

• AP = 5 , 9 , 13 , 17 OR 17 , 13 , 9 , 5

• There are two AP's available here because we cannot say whether common difference ( d ) is positive or negative unless it is given in question.

Hope it helps you