If an arithmetic series starting with 5 has a sum of 3925 of its first 50 terms, what is the common difference?

(type number only in box)

Question

If an arithmetic series starting with 5 has a sum of 3925 of its first 50 terms, what is the common difference?

(type number only in box)

BlackTom AI · Accepted Answer

We are given an arithmetic sequence with first term a1 = 5 and an unknown common difference d. The sum of the first n = 50 terms is S50 = 3925.

Use the sum formula for an arithmetic series: S_n = n/2 [2a1 + (n - 1)d]. Substituting the known values,
S50 = 50/2 [2(5) + (50 - 1)d] = 25 [10 + 49d].

Set this equal to the given sum: 25 [10 + 49d] = 3925.

Divide both sides by 25 to simplify: 10 + 49d = 3925 / 25. Compute 3925 ÷ 25 = 157.

Now solve for d: 49d = 157 − 10 = 147, so d = 147 / 49 = 3.

Thus, the common difference is 3.

If an arithmetic series starting with 5 has a sum of 3925 of its first 50 terms, what is the common difference? (type number only in box)

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