Question

Question 12 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.

Class X1 - Maths -Sequences and Series Page 199

Answer 1

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

Answer 2

Step-by-step explanation:

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