Question

the amount of money in the money box of them a's daughter on 1st 2nd 3rd 4th birthday. . .. were 1000,1500,2000,2500.......then the total money on her 21st birthday

Answer 1

the answer is 11000 the answer

Answer 2

Given are the amounts of money in the box for birthdays, Find the amount of money in the box on the twenty-first birthday.

Explanation:

• Given are the amounts of money in the money box for $1^{st},\ 2^{nd},\ 3^{rd}\ and\ 4^{th}$ birthdays.
• Let the corresponding amounts of money be denoted by $m_1,\ m_2,\ m_3....m_n$.
• Then we have, $m_1=1000,\ \ m_2=1500,\ \ m_3=2000,\ \ m_4=2500$  
• Now in $m_1,m_2..\ m_n$ we have $m_2-m_1=m_3-m_2=m_4-m_3=500$.
• Hence, the amounts of money are in an arithmetic progression where $a=m_1=1000,\ \ \ d=500$
• Now for the nth term of an A.P we have, $m_n=a+(n-1)d$
• Hence the amount of money in the box on $21^{st}$ birthday is,  $->m_{21}=m_1+(n-1)d\\->m_{21}=1000+(21-1)500\\->m_{21}=11,000$  
• Therefore the amount of money in the money box on her $21^{st}$ birthday is $Rs.\ 11,000$.