Question

IF 2nd term of a GP is $16$ and 5th term is $1024$, find the GP____.

• A. (4,-16,64,-256,1024)
• B. (6,-16,96,-250,1024)
• C. (8,-16,32,-264,1024)
• D. (-6,-16,64,256,1024)

Answer 1

The correct option is A (4,-16,64,-256,1024)

Given,

$t_2=16,t_5=1024$

let a be the first terms and r be the common ratio

then

$ar=16,a{r}^4=1024$

$\frac{a{r}^4}{ar}=\frac{1024}{16}\to r^3=64\to r=\pm 4$

If r=4

$a\times 4=16,a=4$

if r=-4

$a\times -4=16,a=-4$

Required GP is (4,16,64,...)

if r=-4

GP is (4,-16,64,-256,.....)