Write first four terms of the A.P. when the first term a and the common difference are given as follows:
(i) a = 10, d = 10
(ii) a = -2, d = 0
(iii) a = 4, d = – 3
(iv) a = -1 d = 1/2
(v) a = – 1.25, d = – 0.25
Answers
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General form of an AP.:
a, a+d, a+2d, a+3d…….
Here a is the first term and d is common difference.
Solution:
(i) Given:a = 10, d = 10
Let the series be a1, a2, a3, a4, a5 …
a1 = a = 10
a2 = a1 + d = 10 + 10 = 20
a3 = a2 + d = 20 + 10 = 30
a4 = a3 + d = 30 + 10 = 40
a5 = a4 + d = 40 + 10 = 50
the series will be 10, 20, 30, 40, 50 …
First four terms of this A.P. will be 10, 20, 30, and 40.
(ii)Given: a = – 2, d = 0Let the series be a1, a2, a3, a4 …
a1 = a = -2
a2 = a1 + d = – 2 + 0 = – 2
a3 = a2 + d = – 2 + 0 = – 2
a4 = a3 + d = – 2 + 0 = – 2
the series will be – 2, – 2, – 2, – 2 …
First four terms of this A.P. will be – 2, – 2, – 2 and – 2.
(iii) Given:a = 4, d = – 3Let the series be a1, a2, a3, a4 …
a1 = a = 4
a2 = a1 + d = 4 – 3 = 1
a3 = a2 + d = 1 – 3 = – 2
a4 = a3 + d = – 2 – 3 = – 5
the series will be 4, 1, – 2 – 5 …
First four terms of this A.P. will be 4, 1, – 2 and – 5.
(iv) Given:a = – 1, d = 1/2Let the series be a1, a2, a3, a4 …a1 = a = -1
a2 = a1 + d = -1 + 1/2 = -1/2
a3 = a2 + d = -1/2 + 1/2 = 0
a4 = a3 + d = 0 + 1/2 = 1/2
the series will be-1, -1/2, 0, 1/2
First four terms of this A.P. will be -1, -1/2, 0 and 1/2.
(v)Given: a = – 1.25, d = – 0.25Let the series be a1, a2, a3, a4 …
a1 = a = – 1.25
a2 = a1 + d = – 1.25 – 0.25 = – 1.50
a3 = a2 + d = – 1.50 – 0.25 = – 1.75
a4 = a3 + d = – 1.75 – 0.25 = – 2.00
the series will be 1.25, – 1.50, – 1.75, – 2.00 ……..
First four terms of this A.P. will be – 1.25, – 1.50, – 1.75 and – 2.00.
SOLUTION :-
(i) a = 10, d = 10
•Let us consider, the Arithmetic Progression series be a1, a2, a3, a4, a5 …
=>a1 = a = 10
=>a2 = a1+d = 10+10 = 20
=>a3 = a2+d = 20+10 = 30
=>a4 = a3+d = 30+10 = 40
=>a5 = a4+d = 40+10 = 50
And so on…
Therefore, the A.P. series will be 10, 20, 30, 40, 50 …
And First four terms of this A.P. will be 10, 20, 30, and 40.
(ii) a = – 2, d = 0
•Let us consider, the Arithmetic Progression series be a1, a2, a3, a4, a5 …
=>a1 = a = -2
=>a2 = a1+d = – 2+0 = – 2
=>a3 = a2+d = – 2+0 = – 2
=>a4 = a3+d = – 2+0 = – 2
Therefore, the A.P. series will be – 2, – 2, – 2, – 2 …
And, First four terms of this A.P. will be – 2, – 2, – 2 and – 2.
(iii) a = 4, d = – 3
•Let us consider, the Arithmetic Progression series be a1, a2, a3, a4, a5 …
=>a1 = a = 4
=>a2 = a1+d = 4-3 = 1
=>a3 = a2+d = 1-3 = – 2
=>a4 = a3+d = -2-3 = – 5
Therefore, the A.P. series will be 4, 1, – 2 – 5 …
And, First four terms of this A.P. will be 4, 1, – 2 and – 5.
(iv) a = – 1, d = 1/2
•Let us consider, the Arithmetic Progression series be a1, a2, a3, a4, a5 …
=>a2 = a1+d = -1+1/2 = -1/2
=>a3 = a2+d = -1/2+1/2 = 0
=>a4 = a3+d = 0+1/2 = 1/2
Thus, the A.P. series will be-1, -1/2, 0, 1/2
And First four terms of this A.P. will be -1, -1/2, 0 and 1/2.
(v) a = – 1.25, d = – 0.25
•Let us consider, the Arithmetic Progression series be a1, a2, a3, a4, a5 …
=>a1 = a = – 1.25
=>a2 = a1 + d = – 1.25-0.25 = – 1.50
=>a3 = a2 + d = – 1.50-0.25 = – 1.75
=>a4 = a3 + d = – 1.75-0.25 = – 2.00
Therefore, the series will be 1.25, – 1.50, – 1.75, – 2.00 ……..
And first four terms of this A.P. will be – 1.25, – 1.50, – 1.75 and – 2.00.