Question

Write the first four terms of the sequence defined by An=20-30(n-1)

Answer 1

The first four terms of sequence is 20, -10, -40, -70

Solution:

Given that we have to find the first four terms of sequence

Given recursive formula is:

`a_n = 20 - 30(n-1)`

To find the first term, substitute n = 1

`a_1 = 20-30(1-1)\\\\a_1 = 20-30(0)\\\\a_1 = 20`

Thus the first term of sequence is 20

To find the second term, substitute n = 2

`a_2 = 20-30(2-1)\\\\a_2 = 20-30(1)\\\\a_2 = 20-30\\\\a_2 = -10`

Thus the second term of sequence is -10

To find the third term, substitute n = 3

`a_3 = 20-30(3-1)\\\\a_3 = 20-30(2)\\\\a_3 = 20-60\\\\a_3 = -40`

Thus the third term of sequence is -40

To find the fourth term, substitute n = 4

`a_4 = 20-30(4-1)\\\\a_4 = 20-30(3)\\\\a_4 = 20-90\\\\a_4 = -70`

Thus the first four terms of sequence is 20, -10, -40, -70