For the AP: -3, -7, -11, ..., can we find directly a₃₀ - a₂₀ without actually finding a₃₀ and a₂₀? Give reasons for your answer
Solution:
True,
An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.
The nth term of an AP,
aₙ = a + (n - 1)d.
a₃₀ = a + (30 - 1 )d
a₃₀ = a + 29d
a₂₀ = a + (20 -1)d
a₂₀ = a + 19d ………… (1)
a₃₀ - a₂₀ = (a + 29d) - (a + 19d)
a₃₀ - a₂₀ = 10d
From the question above,
d = -7 - (-3) = -7 + 3 = -4
From (1), we get,
a₃₀ - a₂₀ = 10(-4)
a₃₀ - a₂₀ = -40.
Therefore, a₃₀ - a₂₀ = -40.
✦ Try This: Which term of the progression 4, 9, 14, 19, … is 109
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.2 Problem 3
For the AP: -3, -7, -11, ..., can we find directly a₃₀ - a₂₀ without actually finding a₃₀ and a₂₀? Give reasons for your answer
Summary:
For the AP: -3, -7, -11, ...,a₃₀ - a₂₀ without actually finding a₃₀ and a₂₀ is -40
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