If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term
a. 30
b. 33
c. 37
d. 38
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.
From the question, we get,
a₂ = a + d = 13----------------(1)
a₅ = a + 4d = 25---------------(2)
Arranging equation (1) we have,
a = 13 - d
Substituting (1) in (2), we have,
13 - d + 4d = 25
13 + 3d = 25
3d = 12
d = 4.
Put d = 4 in (1), we get,
a = 13 - 4
a = 9.
For the 7th term,
a₇ = a + 6d
a₇ = 9 + 6(4)
a₇ = 9 + 24 = 33
a₇ = 33.
Therefore, a₇ = 33.
✦ Try This: Which term of the AP 3, 8, 13, 18,... is 78
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.1 Problem 7
If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term, a. 30, b. 33, c. 37, d. 38
Summary:
An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. If the 2nd term of an AP is 13 and the 5th term is 25, its 7th term is 33.
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