Share

# Find the Next Five Terms of the Following Sequences Given by A_1 = 1, A_N = A_(N - 1) + 2, N >= 2 - CBSE Class 10 - Mathematics

#### Question

Find the next five terms of the following sequences given by

a1 = a2 = 2, an = an−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

a1 = a2 = 2, an = an−1 − 3, n > 2

Here, we are given that n > 2

So, the next five terms of this A.P would be a_3, a_4, a_5, a_6, a_7

Now a_1 = a_2 = 2 ....(1)

So, to find the a_3term we use n = 3  we get

a_3 = a_(3 -1) - 3

a_3 = a_2 - 3

a_3 = 2 - 3 (using 1)

a_3 = -1 ......(2)

For a_4 using n = 4 we get

a_4 = a_(4 -1) - 3

a_4 = a_3 - 3

a_4 = -1-3 (using 2)

a_4 = -4 ....(3)

For a_5 using n = 5 we get

a_5 = a_(5 -1) - 3

a_5 = a_4 - 3

a_5 = -4 -3  (Using 3)

a_5 = -7 ...(4)

For a_6 using n = 6 we get

a_6 = a_(6 -1) - 3

a_6 = a_5 - 3

a_6 = -7 - 3 (Using 4)

a_6  = -10 ......(5)

For a_7 using n= 7 we get

a_7 = a_(7 - 1) - 3

a_7 = a_6 - 3

a_7 = -10 - 3 (Using 5)

a_7 = -13

Therefore, the next five terms, of the given A.P are

a_3 = -1, a_4 = -4, a_5 = -7, a_6 = -10, a_7 = -13`

Is there an error in this question or solution?

#### APPEARS IN

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