In an A.P., given l = 28, S = 144, and there are total 9 terms. Find a.

By formula,

Sum of n terms = $\dfrac{n}{2}$ [First term + Last term]

Given,

n = 9 and l = 28.

S₉ = 144

Substituting values we get :

$\Rightarrow \dfrac{9}{2}[a + 28] = 144 \\[1em] \Rightarrow a + 28 = \dfrac{144 \times 2}{9} \\[1em] \Rightarrow a + 28 = 16 \times 2 \\[1em] \Rightarrow a + 28 = 32 \\[1em] \Rightarrow a = 32 - 28 = 4.$

Hence, a = 4.