A ladder has 15 tapered rungs, the lengths of which increase by a common difference. The first rung is 5 inches long, and the last rung is 20 inches long. What is the sum of the lengths of the rungs?

Expert Solution

Consider a ladder with 15 tapered rungs. The lengths of rungs are increasing by a common difference. First rung is 5 inches long and last rung is 20 inches long.

So, the lengths of rungs make an arithmetic sequence with a1 = 5 and a15 = 20.

Use the formula for the sum of first n terms of an arithmetic sequence,

Sn = n(a1 + an)/2 ...... (1)

Substitute n = 15, a1 = 5 and a15 = 20 in the formula (1) and simplify,

S15 = 15(5 + 20)/2

= 15 × 25/2

= 187.5

Therefore, sum of the lengths of the rungs is 187.5 inches.

Junaid answered 1 year ago

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Question

A ladder has 15 tapered rungs, the lengths of which increase by a common difference. The first rung is 5 inches long, and the last rung is 20 inches long. What is the sum of the lengths of the rungs?

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Expert Solution

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