Question:
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
Answer:
Let total number of terms in AP is n, first term is a and common difference is d.
Given a =11
Let the AP is a, a+d, a+2d, a+3d,........a+(n-2)*d, a+(n-1)*d
Sum of four terms = 56
=> a+(a+d)+(a+2d)+(a+3d) = 56
=> 4a +6d = 56
=>4*11 +6d = 56
=>44 +6d = 56
=>6d = 56-44
=>6d = 12
=>d = 12/6
=> d=2
Sum of last four terms = 112
=> a+(n-4)*d + a+(n-3)*d + a+(n-2)*d + a+(n-1)*d = 112
=>4a +nd - 4d + nd - 3d + nd - 2d + nd - d = 112
=>4a + 4nd - 10d = 112
=>4*11 + 4n*2 - 10*2 = 112
=>44 + 8n - 20 = 112
=>24 + 8n =112
=>8n = 112-24
=>8n = 88
=>n = 88/8
=>n = 11
So number of term in AP = 11
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