Three numbers are in AP there sum is 48 and product of 1st and 3rd term is 175.find the number
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Three numbers are in AP there sum is 48 and product of 1st and 3rd term is 175.find the number
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Answer:
Step-by-step explanation:
Let the required numbers be (a - d), a and (a + d).
It is given that ;
Sum of numbers is 21.
⇒ a - d + a + a + d = 21
⇒ 3a = 48
⇒ a =
⇒ a = 16
Also, the product of first and third term is 175.
⇒ (a - d) * (a + d) = 175
⇒ (a² - d²) = 175
⇒ (16² - d²) = 175
⇒ 256 - d² = 175
⇒ d² = 256 - 175
⇒ d² = 81
⇒ d = ± √81
⇒ d = ± 9
Thus, a = 16 and d = ± 9.
The required numbers are;
(a - d) = (16 - 9) = 7
a = 16
(a + d) = 16 + 9 = 25
Or, the other possibility can be -
(a - d) = 16 + 9 = 25
a = 16
(a + d) = 16 - 9 = 11
Hence, the required numbers in an AP are (7, 16, 25) or (25, 16, 7).
Verified answer
Let the first 3 terms of the A.P be a-d, a and a+dby data, (a-d) + a + (a+d)= 48
3a=48
a=16
as per data: (a-d)*a= 4(a+d)+12--(1)
substituting the value of 'a' in (1); (16-d)*16=4(16+d) +12
256 - 16d = 64 + 4d + 12
256 - 16d =76 + 4d
256-76= 16d+4d
180 = 20d
d= 9