Question

The sum of four consecutive number in an AP is 32and the ratio of the product of the first and the last term to two middle terms is 7:15.Find the numbers

Answer 1

please see the attached picture for answers

Answer 2

Hii friend,


LET the four consecutive terms of AP be (a-3d), ( a-d) , (a+d) , ( a+3d).

A/Q,

a-3d + a-d + a + d + a + 3d = 32

4a = 32

a = 32/4 = 8 .

And,

(a-3d) × (a+3d) / (a-d) × (a+d) = 7/15

a² - 3d² / a²- d². [ (a+b) × (a-b) = a2 - b²]

PUTTING THE VALUE OF A IN,

a²-3d² / a² - d² = 64-3d²/64 - d² = 7/15

SOLVE THIS U WILL GET THE VALUE OF D...

AND PUT THE VALUE OF A AND D IN ALL FOUR CONSECUTIVE TERMS OF THE AP...THEN U WILL GET ALL THE NUMBERS....

HOPE U WILL UNDERSTAND THIS....