In an AP if a = -7.2, d = 3.6, aₙ= 7.2, then n is
a. 1
b. 3
c. 4
d. 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.
Considering the question, we get the values as,
aₙ = a + (n−1)d.
7.2 = -7.2 + (n - 1) (3.6)
7.2 = -7.2 + (3.6n - 3.6)
7.2 + 7.2 + 3.6 = 3.6n
18 = 3.6n
n = 5.
Therefore, n = 5.
✦ Try This: Find the nth term of AP: 1, 2, 3, 4, 5…., an, if the number of terms are 15
The nth term of an AP is
aₙ = a + (n - 1 )d.
a = first term
aₙ = nth term
d = common difference.
The AP given is 1, 2, 3, 4, 5…., an
a = 1
n = 15
d = 2 - 1 = 1
a15 = 1 + (15 - 1) 1
a15 = 1 + 14
a15 = 15
Therefore, the nth term of AP is 15.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.1 Sample Problem 2
In an AP if a = -7.2, d = 3.6, aₙ= 7.2, then n is, a. 1, b. 3, c. 4, d. 5
Summary:
An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. In an AP if a = -7.2, d = 3.6, an = 7.2, then n is 5
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