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Find the four terms of the arithmetic sequence given the 13th term (a_{13}=-60) and the thirty third term (a_{33}=-160).Given terms: a_{13}=-60 and a_{33}= -160Find these terms:a_{14}= Answera_{15}= Answera_{16}= Answera_{17}= Answer

Find the four terms of the arithmetic sequence given the 13th term a1360 and the thirty third term a33160Given terms a1360 and a33 160Find these termsa14 Answer class=

Respuesta :

Given:

13th term = -60

33rd term = -160

Find:

14th, 15th, 16th, and 17th term

Solution:

For us to determine the 14 - 17th term, we need to identify the common difference in this arithmetic sequence. The formula is:

[tex]\frac{a_{33}-a_{13}}{33-13}[/tex]

Let's plug in the values of a₃₃ and a₁₃ in the formula above.

[tex]\frac{-160-(-60)}{33-13}[/tex]

Then, solve.

[tex]\frac{-100}{20}=-5[/tex]

Hence, the common difference between the terms is -5.

So, the next 4 terms after a₁₃ are shown below:

[tex]\begin{gathered} a_{14}=-65 \\ a_{15}=-70 \\ a_{16}=-75 \\ a_{17}=-80 \end{gathered}[/tex]

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