The sum of three numbers in A.P. is 27 and their product is 405 then common difference is
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Answer: HOPE THIS HELPS YOU, MARK BRAINLIST AND THANK.
Step-by-step explanation: D = 6
Let's Take The Numbers which are in AP :
a-d , a , a + d
We Have Sum Of These Numbers is equal to 27
a - d + a + a + d = 27
3a = 27
a = 9
And Now We have Their Product Is Equal to 405
(a - d) * (a+d) * a = 405
Putting the value of a = 9,
(9 - d) * (9 + d) * 9 = 405
(9 - d) * (9 + d) = 45
81 - d² = 45
d² = 81 - 45
d² = 36
d=√36
∴d=6
So, D = 6
Answer:
Step-by-step explanation:
- The 3 numbers are in A.P
- Sum is 27
- Product is 405
- Common difference (d)
→ Since the numbers are in A.P, let the numbers be,
a - d, a, a + d
→ Given that their sum is 27, hence adding it
a - d + a + a + d = 27
→ Here d gets cancelled
a + a + a = 27
3a = 27
a = 9
→ Also it is given that the product of numbers is 405
(a - d) × a × ( a + d ) = 405
→ Substitute the value of a above
( 9 -d )× 9 ×( 9 + d) = 405
→ Applying the identity ( a + b) (a - b) = a² - b²
9 × (9²-d²) = 405
81 - d² = 405/9
-d² = 45 - 81
d² = 36
d = √36
d = ± 6
→ Hence common difference is ±6
→ Case 1 : If a is 9, d is 6
First number = a - d = 9 - 6 =3
Second number = a = 9
Third number = a + d = 15
3 + 9 + 15 = 27
3 × 9 × 15 = 405
Hence verified
→ Case : 2
If a is 9, d is -6
First number = a - d = 9 + 6 = 15
Second number = a =9
Third number = a + d = 9 -6 = 3
15 + 9 + 3 = 27
15 × 9 × 3 = 405
Hence verified
→ The common difference of an A.P is the difference between its two consecutive terms.
d = a₂ - a₁