If the nth term of the A. P. 9, 7, 5.... is same as the nth term of the A. P. 15, 12, 9...... find n.
Answers
Answer:
Series 1: - 9 , 7,5,3.............
Difference = 2 = d
a = beginning term = 9
let t be the nth term
Then t = a-(n-1)×d (- is because as it is in ascending order)
⇒ tn = 9-(n-1)×2 ........................ 1
Series 2 : - 12,9,6,3
difference =d= 3
Let t be the nth term
t = a - (n-1) *d
tn = 12 - (n-1)* 3 ..........................2
eqn 1 = eqn 2
12 - (n-1)3 = 9 -(n-1)2
⇒ 3 = 3n - 3 -2n+2
⇒ 3 +3-2= n
⇒ n= 4 Ans.
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Step-by-step explanation:
Answer:
9,7,5....
a = 9
d = 7 - 9 = -2
nth term= a + (n-1) d
an = 9 + (n-1) (-2)
an = 9n - 9 × -2
an = 9n + 18 .....(i)
15,12,9...
a = 15
d = 12 - 15 = -3
nth term = a + (n-1) d
an = 15 + (n-1) (-3)
an = 15n - 15 × -3
an = 15n + 45 ....(ii)
from (i) & (ii)
9n + 18 = 15n + 45
9n - 15n = 45 - 18
-6n = 27
n = 27/-6
n = 9/-2
Step-by-step explanation:
an = a + (n-1) d
where an = value of nth term
a = first term
n = no. of terms
d = common difference