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Reika [66]
2 years ago
9

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. Find the sum of all ten terms.
Mathematics
1 answer:
poizon [28]2 years ago
4 0

Answer:

\boxed{a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a_{10}=66}

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

a_1+a_2=x\\a_3=x\\a_4=2x\\a_5=3x\\a_6=5x\\a_7=8x\\

We know that:

a_7=6\\\implies 8x=6\\x=\frac{3}{4}

We get:

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}\\

Therefore, we calculate

\boxed{a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8+a_9+a_{10}=66}

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