Question
Download Solution PDFThe sum of the 3rd and the 7th term of an A.P. is 30 and the sum of the 5th and the 9th term is 56. Find the sum of the 4th and the 8th terms of the same series.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The nth number in A.P. series (an) = a + (n-1)d
The sum of the n numbers in the series =
Where 'a' is the first number of the series and 'd' is the common difference
Calculation:
Let the first term of the A.P. be 'a' and the common difference be 'd'
Given a3 + a7 = 30
a + 2d + a + 6d = 30
2a + 8d = 30 ...(i)
Also given a5 + a9 = 56
a + 4d + a + 8d = 56
2a + 12d = 56 ...(ii)
Adding (i) and (ii)
4a + 20d = 86
2a + 10d = 43
a + 3d + a + 7d = 43
a4 + a8 = 43
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