Question

Two A.P.’s are given 9, 7, 5, . . . and 24, 21, 18, . . . . If nth term of both the progressions are equal then find the value of n and nth term. Solve the word problem

Answer 1

Step-by-step explanation:

a+(n-1) d=n^th

9+(n-1)(7-9)=24+(n-1)(21-24)

9+(n-1)(-2)=24+(n-1)(-3)

(-2)(n-1)-(-3)(n-1)=15

n-1=15

n=16

Answer 2

Answer:

n = 16

nth term = -21

Step-by-step explanation:

nth term of an AP is given by

nth Term = a + (n-1)d

1st AP

9 , 7  , 5

a = 9   d = -2

nth Term =   9 + (n-1)(-2)

= 11 - 2n

2nd AP

24 , 21 , 18

a = 24   , d = -3

nth term = 24 + (n-1)(-3)

= 27 - 3n

nth term of both the progressions are equal

11 - 2n = 27-3n

=> n = 16

nth term = 9 + (16-1)(-2) = -21

nth term =  -21