Question 4 (x)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(x) a, 2a, 3a, 4a …

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Solution

(x) $a, 2 a, 3 a, 4 a \dots \dots$
Here,
$a_{2} - a_{1} = 2 a - a = a a_{3} - a_{2} = 3 a - 2 a = a a_{4} - a_{3} = 4 a - 3 a = a$
$\Rightarrow a_{n + 1} - a_{n}$ is same everytime.
Therefore, d=a and the given numbers are in A.P.
Next three terms are:
$a_{5} = 4 a + a = 5 a a_{6} = 5 a + a = 6 a a_{7} = 6 a + a = 7 a$

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Arithmetic Progression

Standard X Mathematics

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Question 4 (x) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (x) a, 2a, 3a, 4a …

(x) a,2a,3a,4a…… Here, a2−a1=2a−a=aa3−a2=3a−2a=aa4−a3=4a−3a=a ⇒an+1−an is same everytime. Therefore, d=a and the given numbers are in A.P. Next three terms are: a5=4a+a=5aa6=5a+a=6aa7=6a+a=7a

Question 4 (x)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(x) a, 2a, 3a, 4a …