the arithmetic mean of first three terms of an ap is 5 find the middle term of an - Maths - Sequences and Series

Question

the arithmetic mean of first three terms of an ap is 5 find the
middle term of an ap

Varun.Rawat · Accepted Answer

Let a1, a2 and a3 be the first terms of AP
now, AM = a1+a2+a33⇒5 = a1+a2+a33⇒a1+a2+a3 = 15⇒a+a+d+a+2d = 15     a = first term; d = common difference⇒3a + 3d = 15⇒a + d = 5number of terms, n = 3Middle term = n+12th term = 3+12th term = 2nd termNow, middle term = a2 = a+d = 5

the arithmetic mean of first three terms of an ap is 5 . find the middle term of an ap