Question

What is the common ratio between successive terms in the sequence? 2, –4, 8, –16, 32, –64, ...

Answer 1

ʜᴇy ᴅᴇᴀʀ ...
ᴜʀ ᴀɴꜱ ɪꜱ ʜᴇʀᴇ ....
⭐ꜱᴇqᴜᴇɴᴄᴇ - An ordered collection of numbers a1 , a2 ,a3 ......an ..........is a sequence .



♠ᴀʀɪᴛʜᴍᴇᴛɪᴄ ᴩʀᴏɢʀᴇꜱꜱɪᴏɴ - A sequence a1, a2,a3,......an is called an Arithmetic progression ( A.P. ) when a2 - a1 = a3 - a2 =........= an - an-1 . That means A.P. is a sequence in which each term is obtained by adding a constant d to the proceding term . This constant d is called common difference of the A.P.



♠ɢᴇᴏᴍᴇᴛʀɪᴄ ᴩʀᴏɢʀᴇꜱꜱɪᴏɴ - If in a sequence of terms each term is constant multiple of the proceeding term then the sequence is called a Geometric progression ( G.P.) .The constant multiplier is called the common ratio .
ᴄᴏᴍᴍᴏɴ ʀᴀᴛɪᴏ = ᴀɴy ᴛᴇʀᴍ / ᴩʀᴇᴄᴇᴇᴅɪɴɢ ᴛᴇʀᴍ
ᴏʀ
= tn / tn -1



ʟᴇᴛ'ꜱ ᴍᴏᴠᴇ ᴛᴏ ᴜʀ qᴜᴇꜱᴛɪᴏɴ ---

ɢɪᴠᴇɴ -
ꜱᴇʀɪᴇꜱ = 2,-4,8,-16,32,-64....
ᴄᴏᴍᴍᴏɴ ʀᴀᴛɪᴏ ???


we know that
common ratio = tn / tn -1

so a2 = -4
a1 = 2

common ratio = -4/2
= - 2

☺hσpє ít hєlpѕ u☺
❤fєєl frєє tσ αѕk αnч quєrч ❤

Answer 2

Given Series,

2, –4, 8, –16, 32, –64, ...

Clearly  this is an G.P.

First  term (T₁) = 2

Second  Term (T₂) = -4

If the  common ration between  the term is  r,

r = T₂/T₁

r = -4/2

r = -2