If the nth terms of the two APs: 9, 7, 5,… and 24, 21, 18,. .. are the same, find the value of n. Also find that term
Solution:
Consider the first term, common difference and number of terms of the AP: 9, 7, 5,…. are
a1, d1 and n1
First term (a1) = 9
Common difference (d1) = 7 - 9 = -2
T’n1 = a1 + (n1 - 1) d
= 9+ (n1 - 1) (-2)
= 9 - 2n1 + 2
T’n1 = 11 - 2n1 ….. (i)
The nth term of an AP is
Tn = a + (n - 1) d
Consider the first term, common difference, and the number of terms of the AP: 24, 21, 18, … are a2, d2, and n2
First term, (a2) = 24
Common difference (d2) = 21 - 24 = -3
The nth term T’’n2 = a2 + (n2 - 1)d2
T”n2 = 24 + (n2 - 1) (-3)
T”n2 = 24 - 3n2 + 3
T”n2 = 27 - 3n2 …. (ii)
From the given condition the nth term of both AP is same
11 - 2n1 = 27 - 3n2
So we get
n = 16
The nth term of first AP is
T’n1 = 11 - 2n1 = 11 - 2 (16) = 11 - 32 = -21
The nth term of second AP is
T”n2 = 27 - 3n2 = 27 - 3 (16) = 27 - 48 = -21
Therefore, the value of n is 16 and that term i.e., nth term is -21.
✦ Try This: If the nth terms of the two APs: 11, 8, 5,… and 25, 23, 21,. .. are the same, find the value of n. Also find that term
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 14
If the nth terms of the two APs: 9, 7, 5,… and 24, 21, 18,. .. are the same, find the value of n. Also find that term
Summary:
If the nth terms of the two APs: 9, 7, 5,… and 24, 21, 18,. .. are the same, the value of n is 16. Also, that term is - 21
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