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Answer :
Final answer:
a) The rule for the total weight is W_n = 100 + (n - 1)2. b) Based on your 5th lift, the maximum you can lift is 108 pounds. c) Your coach will have done 29 lifts until he surpasses 157 pounds.
Explanation:
a) The rule for the total weight can be represented by an arithmetic sequence, where each term is obtained by adding 2 to the previous term. We can use the formula for the nth term of an arithmetic sequence to write the rule: Wn = W1 + (n - 1)d, where Wn is the weight on the nth lift, W1 is the weight on the first lift (100 pounds), n is the number of lifts, and d is the common difference between the terms (2 pounds). So, the rule is Wn = 100 + (n - 1)2.
b) If you were unable to lift the weight on your 6th lift, it means that the weight on the 5th lift was the maximum weight you could lift. To find this weight, we can substitute n = 5 into the formula: W5 = 100 + (5 - 1)2 = 100 + 4(2) = 108 pounds.
c) To determine how many lifts your coach will have done until he surpasses 157 pounds, we need to find the value of n that satisfies the inequality Wn > 157. We can rearrange the formula to solve for n: n = (Wn - 100)/2. Substituting Wn = 157, we have n = (157 - 100)/2 = 28.5. Since you can't have a fraction of a lift, we round up to the nearest whole number. So, your coach will have done 29 lifts until he surpasses 157 pounds.
Learn more about arithmetic sequences here:
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