An Arithmetic Progression (AP) displays numbers that increase or decrease by a constant difference. The first term initiates the sequence while common difference establishes the pattern throughout. Each subsequent term adds the fixed difference to its previous number. The sum of AP helps calculate series totals for practical applications. Last term marks sequence completion.
Finding missing terms requires understanding pattern relationships. The nth term formula enables value prediction at specific positions. Arithmetic mean connects consecutive terms and helps locate in-between numbers through calculations and properties.
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Given terms in A.P.: 18, a, b, -3
We’ll find the common difference (d):
Since we have 4 terms, and first & last terms are given:
18 + d = a (1st equation)
a + d = b (2nd equation)
b + d = -3 (3rd equation)
Total difference from first to last term = 3d
Thus:
18 – (-3) = 3d
21 = 3d
d = -7
Now, putting d = -7 in equations:
From 1st equation:
18 + (-7) = a
a = 11
From 2nd equation:
11 + (-7) = b
b = 4
Thus: a + b = 11 + 4 = 15