Answer:
The first four terms of the sequence are : 19, 16.5 , 14 , 11.5
Step-by-step explanation:
In the given sequence:
a(3) = 14, a(9) = -1
The general term of a sequence in Arithmetic Progression is:
a(n) = a + (n-1)d
a(3) = a + (3 -1) d = a + 2 d
and a(9) = a + (9- 1 ) d = a + 8 d
⇒ a + 2 d = 14 ......... (1)
and a + 8 d = -1 ........... (2)
Now, solving the given system of equation, we get:
From (1), a = 14 - 2 d
Put in (2), we get:
a + 8 d = -1 ⇒ 14 - 2 d + 8d = -1
⇒ 14 + 6d = -1
or, 6d = -1 -14 = -15
⇒ d = -15/6 = -2.5
or, d = -2.5
Then a = 14 - 2 d = 14 - 2(-2.5) =14 + 5 = 19, or a = 19
Now, first four terms of the sequence is:
a = 19
a(2) = a + 4 = 19 - 2.5 = 16.5
a(3) = a + 2d = 19 + 2(-2.5) = 19 - 5 = 14
a(4) = a + 3d = 19 + 3(-2.5) = 19 - 7.5 = 11.5
Hence, the first four terms of the sequence are : 19, 16.5 , 14 , 11.5
