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If the $6^{th}$ and $7^{th}$ term of a geometric sequence are $5$ and $-10$ respectively, what is the $10^{th}$ term?

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Find missing angles in quadrilaterals II

Full solution

Q. If the

6^{th}

and

7^{th}

term of a geometric sequence are

5

and

-10

respectively, what is the

10^{th}

term?

Identify common ratio: Identify the common ratio $r$ using the $6$ th and $7$ th terms. $\newline$ Calculation: $-10 / 5 = -2$ $\newline$ Common ratio, $r = -2$
Calculate $8$ th term: Calculate the $8$ th term using the $7$ th term and the common ratio. $\newline$ Calculation: $-10 \times -2 = 20$ $\newline$ $8$ th term = $20$
Calculate $9$ th term: Calculate the $9$ th term using the $8$ th term and the common ratio. $\newline$ Calculation: $20 \times -2 = -40$ $\newline$ $9$ th term = $-40$
Calculate $10$ th term: Calculate the $10$ th term using the $9$ th term and the common ratio. $\newline$ Calculation: $-40 \times -2 = 80$ $\newline$ $10$ th term = $80$

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