Question16. Given that the three expressions below belong to the first three terms of an arithmetic sequence, find the following: a) Find the value of the of " $x$ " (1 Point) $$t_{1}=3 x \quad t_{2}=4 x+2 \quad t_{3}=6 x-2$$
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17. b) FInd the value of the common difference "d" (1 Point)
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18. c) Find the sum of the first 10 terms ( 1 Point)
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Studdy Solution
To find the sum of the first 10 terms, use the formula for the sum of an arithmetic sequence:
$$S_n = \frac{n}{2} (2a + (n-1)d)$$
Here, $n = 10$, $a = t_1 = 18$, and $d = 8$.
$$S_{10} = \frac{10}{2} (2 \times 18 + (10-1) \times 8)$$ $$S_{10} = 5 (36 + 72)$$ $$S_{10} = 5 \times 108$$ $$S_{10} = 540$$
The value of $x$ is:
$$\boxed{6}$$
The value of the common difference $d$ is:
$$\boxed{8}$$
The sum of the first 10 terms is:
$$\boxed{540}$$