Match the APs given in column A with suitable common differences given in column B Column A Column B
(A₁) 2, - 2, - 6, -10,... (B₁) 2/3
(A₂) a = -18, n = 10, an = 0 (B₂) - 5
(A₃) a = 0, a10 = 6 (B₃) 4
(A₄) a2 = 13, a4 =3 (B₄) - 4
(B₅) 2
(B₆) 1/ 2
(B₇) 5
Solution:
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 is
aₙ = a + (n - 1 )d.
a = first term
aₙ = nth term
d = common difference.
(A₁) : 2, -2, -6, -10,…
Common difference, d = -2 -2 = -4
So, d = -4.
Therefore,(A₁) matches (B₄ ).
(A₂) : aₙ = a + (n- 1 )d
0 = -18 + (10 - 1)d
18 = 9d
Common difference, d = 2
Therefore, (A₂) matches (B₅ ).
(A₃): a₁₀ = 6, a = 0
Since, an = a + (n - 1 )d
a + (10 - 1)d = 6
Since, a = 0
0 + 9d = 6
d = 6/9
d = 2/3
Therefore, (A₃) matches (B₁ )
(A₄): a₂ = 13, a₄ = 3
Since, an = a + (n - 1 )d
a + (2 - 1)d = 13
a + d = 13 ………… (1)
and a4 = 3 ⇒ a + (4 - 1)d = 3
a + 3d = 3 …………. (2)
On subtracting Eq(1) from Eq(2),
we get,
2d = -10
d = 5.
Therefore, (A₄) matches (B₇ ).
✦ Try This: If the 8th term of an A. P. is 31 and the 15th term is 16 more than the 11th term, find the A. P
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 1
Match the APs given in column A with suitable common differences given in column B
Summary:
So the APs given in column A are matched with a suitable common difference given in column B
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