Question

Question :-

Decide whether the given sequence is in A.P. and find the common difference and next 3 terms of an A.P.

3,6,9,12,....

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Answer 1

Answer:

Question :-

Decide whether the given sequence is in A.P. and find the common difference and next 3 terms of an A.P.

3,6,9,12,....

Required Answer :-

Given sequence →3,6,9,12,----

Here

a = 3,

d = t2 - t1 = 6 - 3 = 3

d = t3 - t2 = 9 - 6 = 3

Here difference between two consecutive terms is constant

Therefore, given sequence is A.P.

For Next three terms,

t5 = t4 + d

t5 = 12 + 3

t5 = 15

t6 = t5 + d

t6 = 15 + 3

t6 = 18

t7 = t6 + d

t7 = 18 + 3

t7 = 21

Therefore next three terms of a A.P. are 15,18 and 21 respectively.

Hope it help you :)

Be brainly!!

Answer 2

Step-by-step explanation:

=6–3= 3 = d

First term = 3 = a

Second term = a+d = 3+3= 6

Third term = a+2d = 3+2(3) = 9

Nth term = a + (n-1) d

The next three terms after 12 are the 5th, 6th and 7th terms.

5th term = a + (5–1) d

= 3+ (4)3 = 3+12 = 15

6th term = a + (6–1) d

= 3+ (5)3 = 3+15 = 18

7th term = a + (7–1) d

= 3+ (6)3 = 3+18 =21