Answer :
Answer:
[tex]\boxed{a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a_{10}=66}[/tex]
Step-by-step explanation:
We know that in a sequence of ten terms, each term (starting with the third term) is equal to the sum of the two previous terms. The seventh term is equal to 6. Therefore, we have
[tex]a_1+a_2=x\\a_3=x\\a_4=2x\\a_5=3x\\a_6=5x\\a_7=8x\\[/tex]
We know that:
[tex]a_7=6\\\implies 8x=6\\x=\frac{3}{4}[/tex]
We get:
[tex]a_1+a_2=x=\frac{3}{4}\\\\a_3=x=\frac{3}{4}\\\\a_4=2x=\frac{3}{2}\\\\a_5=3x=\frac{9}{4}\\\\a_6=5x=\frac{15}{4}\\\\a_7=8x=6\\\\a_8=13x=\frac{39}{4}\\\\a_9=21x=\frac{63}{4}\\\\a_{10}=34x=\frac{102}{4}\\[/tex]
Therefore, we calculate
[tex]\boxed{a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a_{10}=66}[/tex]