Question

If a1=2 and an=2an-1 find the first 5 sequences

Answer 1

Answer:

The first 5 terms of the sequence are 2, 4, 8, 16 and 32.

Step-by-step explanation:

Given:

$a_{1}$ = 2

$a_{n}$ = 2$a_{n-1}$   -----------------(i)

To get the first 5 terms of the sequence, substitute in turn, n = 1, 2, 3, 4, 5 into equation (i).

The first term (when n = 1) has been given as:

$a_{1}$ = 2

The second term (when n = 2) is given as:

$a_{2}$ = 2$a_{2-1}$

$a_{2}$ = 2$a_{1}$    (but $a_{1}$ = 2 )

=> $a_{2}$ = 2(2)

=> $a_{2}$ = 4

The third term (when n = 3) is given as:

$a_{3}$ = 2$a_{3-1}$

$a_{3}$ = 2$a_{2}$    (but $a_{2}$ = 4 )

=> $a_{3}$ = 2(4)

=> $a_{3}$ = 8

The fourth term (when n = 4) is given as:

$a_{4}$ = 2$a_{4-1}$

$a_{4}$ = 2$a_{3}$   (but $a_{3}$ = 8 )

=> $a_{4}$ = 2(8)

=> $a_{4}$ = 16

The fifth term (when n = 5) is given as:

$a_{5}$ = 2$a_{5-1}$

$a_{5}$ = 2$a_{4}$   (but $a_{4}$ = 16 )

=> $a_{5}$ = 2(16)

=> $a_{5}$ = 32

Therefore, the first 5 terms of the sequence are 2, 4, 8, 16 and 32.