If 5 times the 5ᵗʰ term of an AP is equal to 8 times the 8ᵗʰ term then find its 13ᵗʰ term

Start with two identical amounts. Add the same number to both sides. Subtract equal values from each side. Multiply both parts by matching numbers. Divide everything by identical figures. Whatever changes you make apply them to both sides and the quantities stay equal. Remember that sameness creates balance in mathematics.

An Arithmetic Progression (AP) shows numbers increasing or decreasing by a fixed difference. The first term starts the sequence. Common difference creates the pattern. Each term adds the common difference to the previous number. Sum of AP helps calculate series totals. Last term completes the sequence. Finding missing terms requires pattern understanding. The nth term formula predicts values at specific positions. Arithmetic mean connects consecutive terms and finds in-between numbers.