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