Algebra
Class 10

Arithmetic Progression - nth Term

an=a+(n1)da_n = a + (n-1)d
51015102030405060
aₙ = a + (n-1)d

Adjust Variables

First term (a)
a =
1100
Common difference (d)
d =
-1020

The nth term of an AP where a is first term and d is common difference. Every term differs from the previous by exactly d.

Real-World Applications

Salary increments — If salary increases by ₹5000 every year, predict salary in year n.

Staircase design — Each step rises by the same height; find the height of the nth step.

Seating rows — Theater rows where each row has 3 more seats than the previous.

Savings plan — Depositing ₹100 more each month than the previous month.

Depreciation — Linear depreciation where value decreases by fixed amount yearly.

Medicine dosage — Tapering doses that decrease by a fixed amount daily.

Taxi fares — Base fare plus per-km charge forms an AP.

Cricket scoring — Run rates increasing steadily over overs.

Calendar patterns — Days of the week form an AP (mod 7).

Temperature changes — Linear temperature drop over hours.

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