Correct

继续 vs 接着

/ jìxù vs jiē zhāo /
Strokes

Definition

继续 as a Verb, and 接着 as an Adverb or Conjunction, which both means [continue; carry on; follow].

Example

继续 and 接着, both words indicate continuation, but they are of different parts of speech.
1) In examples ① and ②, 继续 is a verb and 接着 is an adverb, but they both function as the adverbial, so either can be used;

2) When 继续 functions as the predicate, however, the adverb 接着 cannot replace it, examples ③;

3) In addition, though both function as the adverbial, 继续 denotes a stronger sense of continuity. In some sentences, only 继续 can be used, examples ④.
1
bìng
hǎo
hòu
以后
  
,
yòu
继续
  
(
jiēzhāo
接着
  
)
xiě
de
lùnwén
论文
  

He resumed his thesis after he got over.

2
Qǐng
继续
  
(
jiēzhāo
接着
  
)
jiǎng
xià
下去
  

Go ahead, please.

3
jiā
大家
yào
de
shì
事业
继续
xià
下去
  

The unfinished research work should be continued.

4
háo
毫不
sōng
jìnr  
劲儿
  
,
继续
zuò
shìyàn
试验
  
,
zhōng
终于
yǒu
liǎo
jiéguǒ
结果
  

He kept on the experiment without any stopping, and as a result, he made some progress.

接着 is also a conjunction, referring to the following of states or actions.
This usage has nothing in common with 继续.
5
Xiān
tīngjiàn
听见
jiǎoshēng
脚步声
  
,
jiēzhāo
接着
  
,
jiù
yǒurén
有人
qiāomén
敲门
  

There's footstep followed by a knock.

6
Shí
yuè
  
,
zhè
这里
jiù
huì
xiàxuě
下雪
  
,
jiēzhāo
接着
  
,
jiùshì
就是
màncháng
漫长
de
dōngtiān
冬天
  

It snowed at the end of October here, and then it was long harsh winter.

继续 occasionally can be an object but is rarely used in such a way and is rather literary.
7
Zhè
shìjiàn
事件
shì
kǒng
恐怖
huódòng
活动
de
继续
  

The event is the extension of terrorism activities.