We read your photo as:

Find the 10th term of the following sequences: a) 8, 3, -2, -7, ... b) 3, 1, 1/3, 1/9, ...

Mathematics

ScanSolve AI Answer

Answers

2 parts
a
-37
b

16561\frac{1}{6561}

Step-by-step solution

4 steps

3) Find the 10th term of the following sequences

Part a· 2 steps

8, 3, -2, -7, ...

  1. Determine the type of sequence.

    Calculate the difference between consecutive terms:
    3−8=−53 - 8 = -5
    −2−3=−5-2 - 3 = -5
    −7−(−2)=−5-7 - (-2) = -5
    Since there is a common difference, d=−5d = -5, this is an arithmetic sequence. The first term is a1=8a_1 = 8.

  2. Use the formula for the nn-th term of an arithmetic sequence.

    The formula is an=a1+(n−1)da_n = a_1 + (n-1)d. We need to find the 10th term, so n=10n=10.

    a10=8+(10−1)(−5)a_{10} = 8 + (10-1)(-5) a10=8+(9)(−5)a_{10} = 8 + (9)(-5) a10=8−45a_{10} = 8 - 45 a10=−37a_{10} = -37

    The 10th term is −37\boxed{-37}.

Part b

16561\frac{1}{6561}

3, 1, 13\frac{1}{3}, 19\frac{1}{9}, ...

  1. Determine the type of sequence.

    Calculate the ratio between consecutive terms:
    13\frac{1}{3}
    1/31=13\frac{1/3}{1} = \frac{1}{3}
    1/91/3=19×3=39=13\frac{1/9}{1/3} = \frac{1}{9} \times 3 = \frac{3}{9} = \frac{1}{3}
    Since there is a common ratio, r=13r = \frac{1}{3}, this is a geometric sequence. The first term is a1=3a_1 = 3.

  2. Use the formula for the nn-th term of a geometric sequence.

    The formula is an=a1rn−1a_n = a_1 r^{n-1}. We need to find the 10th term, so n=10n=10.

    a10=3(13)10−1a_{10} = 3 \left(\frac{1}{3}\right)^{10-1} a10=3(13)9a_{10} = 3 \left(\frac{1}{3}\right)^9 a10=3⋅1939a_{10} = 3 \cdot \frac{1^9}{3^9} a10=3⋅139a_{10} = 3 \cdot \frac{1}{3^9} a10=339a_{10} = \frac{3}{3^9} a10=139−1a_{10} = \frac{1}{3^{9-1}} a10=138a_{10} = \frac{1}{3^8} a10=16561a_{10} = \frac{1}{6561}

    The 10th term is 16561\boxed{\frac{1}{6561}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp