Question

निम्न श्रेणी का योग फल ज्ञात करो। a) 92+90+88+...........+2, b) 101+99+97+..........+47.​

Answer 1

92+90+88(86) +2

101+99+97+(95) 47.

Answer 2

Answer:

(a) 2162   (b) 2072

Step-by-step explanation:

(a) 92+90+88+...........+2

The given series is in A.P

whose, first term, a= 92

common difference, d= 90-92=88-90= -2

last term, l= 2

l= a+(n-1)d

where n is total number of terms.

2 =92+(n-1)(-2)

n= 46

now, sum of all terms, S=(n/2)[2a+(n-1)d]

                                       =(46/2)[2 x 92+(46-1)(-2)]

                                        =2162

(a) 101+99+97+..........+47

The given series is in A.P

whose, first term, a= 101

common difference, d= 99-101=97-90= -2

last term, l= 47

l= a+(n-1)d

where n is total number of terms.

47 =101+(n-1)(-2)

n= 28

now, sum of all terms, S=(n/2)(2a+(n-1)d)

                                       =(28/2)(2 x 101+(28-1)(-2))

                                        =2072