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Lf the sum of the first 20th term of an arithmetic progression is 210and the first term is 1,fond the common difference.?
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Lf the sum of the first 20th term of an arithmetic progression is 210a...



Given information:
The sum of the first 20 terms of an arithmetic progression is 210.
The first term of the arithmetic progression is 1.

Finding the common difference:
To find the common difference of an arithmetic progression, we will use the formula for the sum of the first n terms of an arithmetic progression:
S_n = n/2 * [2a + (n-1)d]
where:
S_n = sum of the first n terms
a = first term
d = common difference
n = number of terms

Substitute the given values:
Given that S_20 = 210 and a = 1, we can plug these values into the formula:
210 = 20/2 * [2(1) + (20-1)d]
210 = 10 * [2 + 19d]
210 = 20 + 190d
190d = 190
d = 1

Conclusion:
The common difference of the arithmetic progression is 1. This means that each term in the progression increases by 1 compared to the previous term.

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Lf the sum of the first 20th term of an arithmetic progression is 210and the first term is 1,fond the common difference.?
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