Question

The sum of four consecutive numbers in A.P. is 32 and the ration of the product of the first and last terms to the product of two middle terms is 7:15. Find the number.

Answer 1

Solution:-
Let the four consecutive numbers in AP be (a - 3d), (a - d), (a + d) and (a + 3d)
So, according to the question.
a-3d + a - d + a + d + a + 3d = 32
4a = 32
a = 32/4
a = 8 ......(1)
Now, (a - 3d)(a + 3d)/(a - d)(a + d) = 7/15
15(a² - 9d²) = 7(a² - d²)
15a² - 135d² = 7a² - 7d²
15a² - 7a² = 135d² - 7d²
8a² = 128d²
Putting the value of a = 8 in above we get.
8(8)² = 128d²
128d² = 512
d² = 512/128
d² = 4
d = 2
So, the four consecutive numbers are
8 - (3 x 2)
8 - 6 = 2
8 - 2 = 6
8 + 2 = 10
8 + (3 x 2)
8 + 6 = 14
Four consecutive numbers are 2, 6, 10 and 14