Question

if the 9th and the 21st term of an ap are 75 and 183 respectively then find the 15th term

Answer 1

Answer:

Step-by-step explanation:

= 75=a+(9-1)d

=75=a+8d.....(1)

183=a+(21-1)d

183=a+20d.......(2)

subtract eq 2 and 1

108=18d

d=6

75=a+48

a=27

now 15th term=27+14*6

101 ans.

Answer 2

Given:

The ninth term is 75.

The twenty-first term is 183.

To find:

The fifteenth term.

Solution:

The formula of A.P is,

an = a + ( n-1) d

a= initial term

d = common difference

an= nth term

A₉ = A + (9-1) D                         (n=9)

75 = A + 8D

A + 8D = 75                               (equation 1)

A₂₁ = A + (21-1) D                      (n=21)

183 = A + 20 D

A + 20 D = 183                          (equation 2)

Subtracting the equations,

12 D = 108

D= 9

For value of A,  

A + (8× 9) = 75

A + 72 = 75

A = 75-72

A = 3

The fifteenth term is,  

A₁₅ = A + ( 15 – 1 ) D (n=15)

= 3 + (14 × 9)

= 3 + 126

= 129

The fifteenth term of the progression is 129.