A man saved ₹ 7,65,000 in 10 years. In each year, after the first, he saved ₹ 6,000 more than he did in the preceding year. How much did he save in the first seven years?

Total saving in 10 years = ₹ 7,65,000

Each year he saved ₹ 6,000 more than previous year

d = 6000

Let his first year saving be ₹ a.

Number of years (n) = 10

By formula,

$S_n = \dfrac{n}{2}[2a + (n - 1)d]$

Substituting values, we get :

$\Rightarrow 765000 = \dfrac{10}{2}[2a + 9(6000)] \\[1em] \Rightarrow 765000 = 5[2a + 54000] \\[1em] \Rightarrow 765000 = 10a + 270000 \\[1em] \Rightarrow 10a = 765000 - 270000 \\[1em] \Rightarrow 10a = 495000 \\[1em] \Rightarrow a = \dfrac{495000}{10} \\[1em] \Rightarrow a = 49500$

Savings in the first seven years :

$\Rightarrow S_7 = \dfrac{7}{2}[2(49500) + (7 - 1)(6000)] \\[1em] = 3.5[99000 + 6(6000)] \\[1em] = 3.5(99000 + 36000) \\[1em] = 3.5(135000) \\[1em] = ₹ 4,72,500.$

Hence, amount saved in first 7 years = ₹ 4,72,500