Question Use the table to answer the question. This table shows x-values with corresponding variables for y-values. x y 2 a 4 b Use the arithmetic sequence formula an=−8+(n−1)⋅2 to find the missing values in the table. (1 point) Responses a=−12 ; b=−10 a equals negative 12 ; b equals negative 10 a=−15 ; b=−13 a equals negative 15 ; b equals negative 13 a=−6 ; b=−2 a equals negative 6 ; b equals negative 2 a=−10 ; b=−8

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GPT-4o mini · Answer

To find the missing values $ a $ and $ b $ in the table using the arithmetic sequence formula $ a_n = -8 + (n-1) \cdot 2 $, we need to determine the values of $ n $ corresponding to $ x = 2 $ and $ x = 4 $. 1. **Finding $ a $ when $ x = 2 $**: - We need to find $ n $ such that $ x = 2 $. - Since the first term corresponds to $ n=1 $, let’s substitute $ n = 1 $: $$ a_1 = -8 + (1 - 1) \cdot 2 = -8 + 0 = -8 $$ - Thus, $ a $ corresponds to $ n = 1 $, and since $ x=2 $ corresponds to $ n=1 $, we find: $$ a = -8 $$ 2. **Finding $ b $ when $ x = 4 $**: - Next, we find $ n $ such that $ x = 4 $. Observe that if $ x $ increases by 2, we assume that $ n $ increases by 1. - Hence, we set $ n = 2 $: $$ a_2 = -8 + (2 - 1) \cdot 2 = -8 + 2 = -6 $$ - So, $ b $ corresponds to $ n = 2 $, and since $ x=4 $, we find: $$ b = -6 $$ Putting this all together: - $ a = -8 $ - $ b = -6 $ Since none of the provided answer options directly match $ a = -8 $ and $ b = -6 $, based on the options you've presented, you may want to recheck if there was a mistake in the problem or options. For the context of your question: - If we reconsider if we missed anything, here's the summary to validate: - With $ n = 1 $ for $ x=2, \; a = -8 $ - With $ n = 2 $ for $ x=4, \; b = -6 $ Would you like to adjust or proceed further?