Question

The boy took the pen.he began to write.(join using participle)

Answer 1

the boy took the pen and began to write

Answer 2

For getting the required sentence we will blend the provided two sentences . This process of combing to produce a single sentence is known as "synthesis." this term is the antonym for analysis. More elaborately, Synthesis is referred to as combining of  multiple  simple sentences, say two or more to form one new statement. It may result in compound, complex or a simple sentence.

Moreover, the the sentence here is in past tense, so, the resultant statement would be as follows:

"Having taken the pen, the boy began to write."