Question

Mr. Dhanesh saves some amount every month. In first month he saves 7 400
second month +500, third month * 600. etc. In which month will he save
F 2000? Find his total saving in 17 months.
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Answer 1

Answer:

Sn=20400

n=15

Step-by-step explanation:

a=400

d=100

tn=2000

tn=a+(n-1)d

2000=400+(n-1)100

2000-400=100n-100

1600+100=100n

1700÷100=n

n=17

Sn=n÷2 (2a+(n-1)d)

S17=17÷2 (2×400+(17-1)100)

S17=17÷2 (800+1600)

S17=17÷2×2400

S17=17×4800

S17=20400

Answer 2

In seventeenth month, he will save Rs 2000. His total savings at the end of month seventeen is 20,400.

Step-by-step explanation:

Given sequence is an arithmetic progression. So,

                    ⇒ $a_{n} = a + (n-1)d$

Where, n is the no. months = 17

             a is the initial saving = 400

              d is the increment in savings = 100

So,                    

                               ⇒ $a_{n} = 400 + (17-1)\times 100$

                                        ⇒ $a_{n} = 2000$

Total savings at the seventeenth month is

                     ⇒ $S_{n} = \frac{n}{2} ( 2\times a (n - 1) \times d)$

               ⇒ $S_{n} = \frac{17}{2}( 2\times 400 (17 - 1) \times 100)$

                      ⇒ $S_{n}$ = 20400