Question

The sum of the three
terms which are in an
Arithmetic progression is 33. If
the product of the first and
third terms exceeds the second
term by 29, find the
Arithmetic progession
​

Answer 1

Answer:

2 , 11 , 20 (or) 20 , 11 , 2

Step-by-step explanation:

3 term formula- a-d, a, a+d

sum-33

a-d + a + a+d = 33 (-d and +d cancelled)

3a = 33

a = 33/3

a=11

Product of first and third term exceeds second term by 29

(a-d) (a+d) = a+29

a^2-d^2 = a+29 (a+b) (a-b) = a^2-b^2

11^2 - d^2 = 11 + 29

121 - d^2 = 40

-d^2 = 40 - 121

-d^2 = -81

d^2 = 81

d = √81

d= +9 (or) -9

Case 1

If a=11 , d=+9

a-d , a , a+d

11-(+9) , 11 , 11+9

2 , 11 , 20

Case 2

If a=11 , d=-9

a-d , a , a+d

11-(-9) , 11 , 11+(-9)

20 , 11 , 2

Therefore,

the numbers are

2 , 11 , 20

(or)

20 , 11 , 2