Question

find the sum of the series 72+70+68+.........+40 what will be the sum if all the terms increased by 12.5%​

Answer 1

Answer:

1071

Step-by-step explanation:

40+42+......+72 are in AP

First term(a)=40

last term(l)=72

common difference(d)=2

let total numbet of terms be 'n'

l=a+(n-1)d

72=40+(n-1)(2)

72=40+2n-2

74=40+2n

34=2n

n=17 terms

sum of all terms in AP is

S=n/2[a+l]

S=17/2[40+72]

S=17/2[112]

S=17×56

S=952

all numbers are increased by 12.5%

12.5%[40+42+...+72]

12.5/100[952]

(11900)/100

119

Finally total sum of series after increasing each by 12% is

952+119

1071 is answer

Answer 2

Answer :

original sum = 952 ; new sum = 1071

Step -by- step explanation :

72+70+68.........+40

It's an AP

a = 72

d = 70-72 = -2

let nth term of this ap be 40

40 = a +(n-1)d

40 = 72 (n-1)(-2)

40 = 72 -2n +2

2n = 74-40

2n = 34

n = 17

Sn = n/2 {2a + (n-1)d}

= 17/2 { 144-32}

= 17/2(112)

= 56× 17 = 952

Now , when each no. is increased by 12.5% , then the sum of this AP will also be increased by 12.5 % i.e new sum will become 112.5% of the original sum

New sum = 112.5(Sn)/100

= (112.5×952)/100

= 1071