Question

What’s the 13th term i this sequence 32768,16384,8192...

Answer 1

EXPLANATION

Compute the ratios of all the adjacent terms: r=(a_n+1)/(a_n)

`(16384)/(32768)=(1)/(2),\: \quad (8192)/(16384)=(1)/(2)`
`\mathrm{The\: ratio\: of\: all\: the\: adjacent\: terms\: is\: the\: same\: and\: equal\: to}`
`r=(1)/(2)`
`\mathrm{The\: first\: element\: of\: the\: sequence\: is}`
`a_1=32768`
`a_n=a_1\cdot r^(n-1)`
`\mathrm{Therefore,\: the\: }n\mathrm{th\: term\: is\: computed\: by}\:`
`r=(1)/(2),\: a_n=32768\mleft((1)/(2)\mright)^(n-1)`

Hence, the 13th term would be:

`a_(13)=32768((1)/(2))^(13-1)=32768((1)/(2))^(12)=32768\cdot(1)/(4096)=8`

The answer is n_13=8