Question

Given the sequence 8,16,32,64. Which expression would give the thirteenth term?

Answer 1

Solution :

Given sequence :

8 , 16, 32 , 64 ,..

first term ( a ) = 8 ,

a2/a1 = 16/8 = 2 ----( 1 )

a3/a2 = 32/16 = 2 ----( 2 )

( 1 ) = ( 2 ) = 2

Therefore ,

Given sequence is G.P .

Common ratio ( r ) = 2

Now ,

n = 13 ( given )

nth term in G.P = an = ar^n-1

=> a13 = ar^12

= 8 × 2^13

= 2³ × 2^13

= 2^3+13

= 2^16

••••

Answer 2

13th term is 32768

Solution:

Given sequence is:

8 , 16 , 32 , 64

Find the common ratio between terms

$\frac{16}{8} = 2\\\\\frac{64}{32} = 2$

Thus this forms a geometric sequence with common ratio 2

The nth term of Geometric sequence is:

$a_n = a \times r^{n-1}$

Where,

$a_n$ = nth term of sequence

a is the first term of sequence

r is common ratio

From given sequence

a = 8

r = 2

To find: 13th term

n = 13

Substituting we get,

$a_{13} = 8 \times 2^{13-1} \\\\a_{13} = 8 \times 2^{12} \\\\a_{13} = 8 \times 4096 \\\\a_{13} = 32768$

Thus 13th term is 32768

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