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The sum of the 4th and 10th terms of an A.P. is 10 and their product is 24. Find the sum of the first 25 terms of
the A.P
Answers
Answered by
91
- Dividing by 2 on both sides]
- Putting the value of a=5-6d in eq ii ]
- Putting the value of d in eq I]
- Now, calculate 1st 25th terms here]
Hence,
- The sum of 1st 25th term's is 175
Answered by
32
Answer:
S₂₅ = 175 and 75
For [ a = 3 and d = 1 / 3 ] and [ a = 7 and d = - 1 / 3 ] respectively!
Step-by-step explanation:
Given :
t₄ + t₁₀ = 10
= > a + 3 d + a + 9 d = 10
= > 2 a + 12 d = 10
= > a = 5 - 6 d .... ( i )
Also given :
t₄ . t₁₀ = 24
= > ( a + 3 d ) ( a + 9 d ) = 24
Putting values of a = 5 - 6 d from ( i )
= > ( 5 - 3 d ) ( 5 + 3 d ) = 24
= > 5² - 9 d² = 24
= > d² = 1 / 9
= > d = ± 1 / 3
Now putting in first :
= > a = 5 - 6 × 1 / 3
= > a = 3 OR a = 7
Sum of first 25 terms as :
S₂₅ = 25 / 2 ( 6 + 24 / 3 ) and 25 / 2 ( 14 - 24 / 3 )
= > S₂₅ = 25 ( 7 ) and 25 / 2 ( 6 )
= > S₂₅ = 175 and 75
Hence we get required answer!
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