Question

Consider the sequence:
1536,768, 384, 192,96, ---
Determine the 11th term of the sequence.

Answer 1

Answer:

1.5

Step-by-step explanation:

Note there is a common ratio between consecutive terms, that is

768 ÷ 1536 = 0.5

384 ÷ 768 = 0.5

192 ÷ 384 = 0.5

96 ÷ 192 = 0.5

This indicates that the terms form a geometric sequence with

$a_{n}$ = a$(r)^{n-1}$

where a is the first term and r the common ratio

Here a = 1536 and r = 0.5, thus

$a_{11}$ = 1536 × $(0.5)^{10}$ = 1.5

Answer 2

Answer:

Step-by-step explanation:

Let ‘a’ is the first term and ‘r’ is a common ratio

By using formula of G.P

Tn = a.r^n-1

=(1536)(1/2)^11-1

= 2^9 x 3 x 2^ -10

= 3 x 2^9-10

= 3 x 2^-1

= 3/2

11th is 3/2