NCERT Class XI Mathematics - Sequences and Series - Solutions
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Question : 80
Total: 106
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Solution:
Let the three numbers in A.P. be a – d, a, a + d. Then
(a – d) + a + (a + d) = 24 ⇒ 3a = 24 ⇒ a = 8 .....(i)
and (a – d) a (a + d) = 440 ⇒( a 2 – d 2 )
⇒[ 8 2 – d 2 ]
⇒ 64 –d 2 d 2 d 2
Case (i) : If d = 3, then the numbers are 8 – 3, 8, 8 + 3 i.e., 5, 8, 11
Case (ii) : If d = – 3, then the numbers are 8 – ( – 3), 8, 8 + (– 3) i.e., 11, 8, 5
(a – d) + a + (a + d) = 24 ⇒ 3a = 24 ⇒ a = 8 .....(i)
and (a – d) a (a + d) = 440 ⇒
⇒
⇒ 64 –
Case (i) : If d = 3, then the numbers are 8 – 3, 8, 8 + 3 i.e., 5, 8, 11
Case (ii) : If d = – 3, then the numbers are 8 – ( – 3), 8, 8 + (– 3) i.e., 11, 8, 5
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