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Find the Next Five Terms of the Following Sequences Given By: A_1 = A_2 = 2, A_N = A_(N - 1) - 3, N > 2 - CBSE Class 10 - Mathematics

Question

Find the next five terms of the following sequences given by:

a_1 = a_2 = 2, a_n = a_(n - 1) - 3, n > 2

Solution

In the given problem, we are given the first, second term and the nth term of an A.P.

We need to find its next five terms

a_1 = 1, a_n = a_(n - 1) + 2, n >= 2

Here, we are given that n >= 2

So the next five terms of this A.P would be a_2, a_3,a_4 and a_6

Now a_1 =1 ...(1)

So tofind the a_2 term we use  n = 2 we get

a_2 = a_(2 - 1) + 2

a_2 = a_1 + 2

a_2 = 1 + 2   (using 1)

a_2 = 3  ....(2)

For a_3 using n = 3 we get

a_3 = a_(3 -1) + 2

a_3 = a_2 + 2

a_3 = 5  ....(3)

For a_4 usign n = 4 we get

a_4 = a_(4 -1) + 2

a_4 = a_3 + 2

a_4 = 5 + 2    (Using 3)

a_4 = 7 ....(4)

For a_5 using n = 5 we get

a_5 = a_(5 -1) + 2

a_5 = a_4 + 2

a_5 = 7 + 2   (Using 4)

a_5 = 9  ....(5)

For a_6 using n = 6 we get

a_6 = a_(6 - 1) + 2

a_6 = a_5 + 2

a_6 = 9 + 2  using 5)

a_6 = 11

Therefore, the next five terms, of the given A.P are a_2 = 3, a_3 = 5, a_4 = 7, a_5 = 7, a_6= 11

Is there an error in this question or solution?

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Solution Find the Next Five Terms of the Following Sequences Given By: A_1 = A_2 = 2, A_N = A_(N - 1) - 3, N > 2 Concept: nth Term of an AP.
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