in an AP the sum of three consecutive terms is 9 and their product is -165 then find those terms
Answers
Solution :
As per the question , in a certain ap there are three consecutive terms such that their sum is 9 and product is -165.
We have to find those terms.
If the second term is a and the common difference is d .
The terms can be (a-d) , a and (a+d)
Their sum is 9
(a-d) + a + (a+d) = 9
> 3a = 9
> a = 3
The terms become (3-d), 3 , (3+d)
Their product is -165
>> (3-d) × 3 × (3+d) = -165
>> (9-d²) × 3 = 165
>> 9-d² = -165/3 = -55
>> d² = 64
>> d = ±8
The terms are -5, 3, 11 or 11, 3, -5
This is the required answer .
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Step-by-step explanation:
Solution :
As per the question , in a certain ap there are three consecutive terms such that their sum is 9 and product is -165.
We have to find those terms.
If the second term is a and the common difference is d .
The terms can be (a-d) , a and (a+d)
Their sum is 9
(a-d) + a + (a+d) = 9
> 3a = 9
> a = 3
The terms become (3-d), 3 , (3+d)
Their product is -165
>> (3-d) × 3 × (3+d) = -165
>> (9-d²) × 3 = 165
>> 9-d² = -165/3 = -55
>> d² = 64
>> d = ±8
The terms are -5, 3, 11 or 11, 3, -5
This is the required answer .
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