Question

Tell me the answer of Q.4

Answer 1

Answer:

Step-by-step explanation:

Let the our parts are a-3d,a-d,a+d and a+3d.

Then by the given question, 

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

or, 4a=32

or, a=8 and

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

or, a²-9d²/a²-d²=7/15

or, 15a²-135d²=7a²-7d²

or, 15a²-7a²=-7d²+135d²

or, 8a²=128d²

or, 8×8²=128d²

or, d²=8×8×8/128

or, d²=4

or, d=+-2

∴, The four parts are:

when d=2

8-(3×2)=8-6=2

8-2=6

8+2=10

8+(3×2)=14

when d=-2

8-(3×-2)=8+6=14

8-(-2)=8+2=10

8+(-2)=8-2=6

8+(3×-2)=8-6=2

Answer 2

Answer:

Step-by-step explanation:

Let the four parts be (a - 3d), (a - d), (a + d), (a + 3d).

(i) Given,Sum of four parts is 32.

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

⇒ 4a = 32

⇒ a = 8

(ii) Product of extremes to means is 7:15

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

⇒ 15(a - 3d)(a + 3d) = 7(a - d)(a + d)

⇒ 15[a² - 9d²] = 7[a² - d²]

⇒ 15a² - 135d² = 7a² - 7d²

⇒ 8a² = 128d²

⇒ 512 = 128d²

⇒ d² = 4

⇒ d = ±2

When a = 8, d = 2:

a - 3d = 2

a - d = 6

a + d = 10

a + 3d = 14

When a = 8, d = -2:

a - 3d = 14

a - d = 10

a + d = 6

a + 3d = 2

Therefore, the A.P is 2,6,10,14 (or) 14,10,6,2

Hope it helps!