## Register Now

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Morbi adipiscing gravdio, sit amet suscipit risus ultrices eu. Fusce viverra neque at purus laoreet consequa. Vivamus vulputate posuere nisl quis consequat.

## 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.

Print or Save

Sol Case (I)
In an A. P.,
9, 7, 5, .................
∴     a = 9 and d = 7 – 9 = –2
tn = a + (n –1)d
tn = 9 + (n –1) (–2)
tn = 9 – 2n + 2
tn = 11 – 2n                        ...(I)
Case (II)
In an A. P.,
24, 21, 18, ................
a = 24, d = 21 – 24 = –3
tn = a + (n –1)d
tn = 24 + (n –1) (–3)
tn = 24 – 3n + 3
tn = 27 – 3n                       ...(II)
nth term of both the A. P. is same
From (I) and (II)
11 – 2n = 27 – 3n
–2n + 3n = 27 – 11
n = 16                      ...(III)
tn = 11 – 2n [From (I)]
= 11 – 2 × 16 [From (III)]
= 11 – 32
tn = –21
∴     The value of n = 16 and the nth term is –21 which will be same for both the progressions.

Arithmetic Progression September 28 , 2018 0 Comments 93 views