Question

plz... solve this??​

Answer 1

Given :

★  Amit saves 200 in the First Month

★  Amit saves 250 in the Second Month

★  Amit saves 300 in the Third Month and so on.

From the above Pattern, We can notice that Amit saves his money in such a way that his savings are in Arithmetic Progression where the savings in the First Month (200) is the First term (a)

Common Difference is the Difference between Second Month Savings and First Month Savings

$\mathsf{\implies Common\;Difference\;(d) = (250 - 200) = 50}$

We know that :

$\bigstar\;\;\mathsf{Sum\;of\; n\; terms \;in \;an \;A.P \;is \;given \;by : \dfrac{n}{2}[2a + (n - 1)d]}$

The Question is to find the Total Savings in 17 Months. It means we need to find the Sum of 17 Months Savings  ⇒ n = 17

$\mathsf{\implies Sum\;of \;17 \;Months\; Savings = \dfrac{17}{2}[2(200) + (17 - 1)50]}$

$\mathsf{\implies Sum\;of \;17 \;Months\; Savings = \dfrac{17}{2}[400 + (16)50]}$

$\mathsf{\implies Sum\;of \;17 \;Months\; Savings = \dfrac{17}{2}[400 + 800]}$

$\mathsf{\implies Sum\;of \;17 \;Months\; Savings = \dfrac{17}{2}[1200]}$

$\mathsf{\implies Sum\;of \;17 \;Months\; Savings = (17 \times 600)}$

$\mathsf{\implies Sum\;of \;17 \;Months\; Savings = 10200}$

Answer : Amit saves ₹ 10200 in 17 Months