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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.
  • a)
    10
  • b)
    12
  • c)
    11
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
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The sum of the first four terms of an A.P. is 56. The sum of the last ...
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The sum of the first four terms of an A.P. is 56. The sum of the last ...
Let the AP is a , a + d , a + 2d , a + 3d ...
Here,
sum of first four terms = 56
a + (a + d) + (a + 2d) + (a + 3d) = 56
4a + 6d = 56
2a + 3d = 28

Given, first term ( a ) = 11
so, 2 *11 + 3d = 28
3d = 28 - 22 = 6
d = 2

Let last term is Tₙ.
then sum of last four terms = 112
e.g. Tₙ + Tₙ_₁ + Tₙ_₂ + Tₙ_₃ = 112
use formula ,
Tₙ = a + (n - 1)d

a + (n -1)d + a + (n - 1 - 1)d + a + (n -2 - 1)d + a + (n - 3 - 1)d = 112
4a + (n - 1 + n - 2 + n - 3 + n - 4)d = 112
4a + (4n - 10)d = 112
put a = 11 and d = 2
4 *11 + (4n - 10) * 2 = 112
44 + (4n - 10) * 2 = 112
2 * (4n - 10) = 68
4n = 44
n = 11


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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.a)10b)12c)11d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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