Question

A man saves Rs.12,000 during the first year, Rs.16,000 in the second year, Rs.20,000 in the third year. If he continues his savings in this sequence, then in how many years will he save Rs.2,00,000? How much will he save in 10 years?

Answer 1

Answer: Total number of years are 8 years and in 10 years he will save 300000.

Given: First year saving = 12000

Second year saving = 16000

Third year saving = 20000

To Find: how many years will he save Rs.2,00,000? How much will he save in 10 years?

Step-by-step explanation:

Step 1: First year saving = 12000

Second year saving = 16000

Third year saving = 20000

Step 2: The first n terms of the arithmetic sequence are added together to form the sum of the first n terms of AP. The product of the difference between the second and first terms, "d," also known as the common difference, and (n-1), where n is the number of terms to be added, is equal to n divided by 2 times the sum of twice the first term, "a."

Step 3: Common difference = 16000 - 12000 = 4000

First term (a) = 12000

Sum (s) = 200000

As we know that for an A.P sum of first n terms is

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

$200000=\frac{n}{2} [2\times12000+(n-1)\times 4000]\\\\200000=\frac{n}{2} [24000+4000n-4000]\\\\400000=24000n+4000n^2-4000n\\\\4000n^2+20000n-400000=0\\\\n^2+5n-100=0$

After solving the above equation, we get

n= 7.8 and -12.80

Hence, Total number of years are 8 years.

Step 4: For n= 10 total sum will be

$s_n=\frac{n}{2} [2a+(n-1)d]\\\\s_n=\frac{10}{2} [2\times 12000+(10-1)4000]\\\\s_n= 5[24000+36000]\\\\s_n=5 \times60000=300000$

Hence, in 10 years he will save 300000.

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https://brainly.in/question/54975702

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Answer 2

Answer:

kuck samajh nahi aaya [NOT UNDERSTOOD ANYTHING]

Step-by-step explanation:

jisko aata hai vo likh de