Algebra
Class 10

Arithmetic Progression - Sum of n Terms

Sn=n2[2a+(n1)d]S_n = \frac{n}{2}[2a + (n-1)d]
5101520250200400600800100012001400
Sₙ = (n/2)[2a + (n-1)d]

Adjust Variables

First term (a)
a =
150
Common difference (d)
d =
-510

Sum of first n terms of an AP. Also written as Sₙ = n/2(a + l) where l is the last term.

Real-World Applications

Gauss's childhood sum — Sum of 1 to 100 = 100×101/2 = 5050.

Total savings — Sum of monthly deposits that increase by a fixed amount.

Stadium seating — Total seats when each row has more seats than the previous.

Loan repayment — Total amount paid with increasing EMIs.

Training programs — Total hours when daily practice increases progressively.

Distance traveled — Object with constant acceleration; sum of distances each second.

Pyramid blocks — Total blocks when each layer has fewer blocks.

Commission calculation — Salesperson with increasing monthly targets.

Fuel consumption — Total fuel used with linearly increasing consumption.

Concert ticket revenue — Different priced rows in a concert hall.

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