Question

The sequence {Aₓ} is defined by A₁ = 2 and Aₓ₊₁ = Aₓ + 2x. What is the value of A₁₀₀.
a.9902 b.9900 c. 10100 d.. 9904

Answer 1

u have
a1=2
a2=2+2
a3=4+4
a4=8+6
a5=14+8

a100= a99+2X99

look for the 1st term on RHS

Answer 2

do u find any pattern?

Answer 3

2,4,8,14,22,32....

Answer 4

do u find any pattern in this sequence?

Answer 5

no thats why i am not getting it

Answer 6

see the difference of consecutive terms...

Answer 7

yes its 2 4 6 8 10

Answer 8

so these r in AP...right?

Answer 9

yes so

Answer 10

s= 2+4+8+14+22+32+............+a99
s= 2+4+ 8 +14+22+32+......+a98+a99

Answer 11

subtract these two

Answer 12

0= 2+2+4+6+..........+(a99-a98) -a99

Answer 13

right?

Answer 14

yes

Answer 15

so a99= 2+2+4+6+..........+(a99-a98)

Answer 16

now u can find a99?

Answer 17

nop

Answer 18

since RHS is an AP so u have to find the sum of an AP for getting the value of a99

Answer 19

2+2+4+6+..........+(a99-a98)
a99=2+(2+4+6+ ....98 terms)

Answer 20

simply put value of x =99 that is
a100 = a99+198.
now u can find an a99 by using an formula of AP on series of a1, a2,a3,a4,a5.
and get a99
and put tha value of a99 in a100 and get your result.

Answer 21

a99= 2+ 98/2{ 2*2 +(98-1)2}

Answer 22

does it help u?

Answer 23

a99=9800

Answer 24

check it

Answer 25

no ..there was a mistake

Answer 26

it should be :
a100 = 2 + {s99} = 2 + 9900

Answer 27

yes it will be 9902

Answer 28

with s99 = 99/2 (2+198)