Question

Show that the progression -1,1/4,3/2,11/4..... is an AP . Find its nth term​

Answer 1

Answer:

CONCEPT OF ARITHMETIC PROGRESSIONS , FOUR FUNDAMENTAL OPERATIONS , GENERAL TERM FORMULA .

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Answer 2

We can find if the common difference is same for the terms :

Here t1 = -1, t2 = 1/4, t3 = 3/2, t4 = 11/4

Common difference d = t(n+1) - tn

For n = 1

d = t2 - t1 = 1/4 - (-1) = 1/4 + 1 = 5/4

For n = 2

d = t3 - t2 = 3/2 - 1/4 = (6-1)/4 = 5/4

For n = 3

d = t4 - t3 = 11/4 - 3/2 = (11-6)/4 = 5/4

Here t2 - t1 = t3 - t2 = t4 - t3 = 5/4

Hence the common difference d is same for all the terms.

So, the given progression is in A.P. ✔✔

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