Question

How many terms at least of the A.P 1,4,7,10,.... are needed to get a sum greater than 590?
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ANSWER: n=21

Answer 1

know the formula for sum of AP ?

Answer 2

yup

Answer 3

S=n/2(2a+(n-1)d)
The Sum should be greater than 590
590<n/2(2a+(n-1)d)
Here a=1,d=3
Substitute and find n...

Answer 4

Sn=n/2[2a+(n-1)d]

Answer 5

yes, that ^

Answer 6

where r u stuck ?>

Answer 7

i cant understand the question

Answer 8

how will i do it to get sum greater than 590

Answer 9

plug in S = 590 , a=1,d= 3 in the formula.

Answer 10

sum greater than 590 --->Sn > 590

Answer 11

n/2[2a+(n-1)d] > 590

Answer 12

Then u will get fraction in n.........might be be....somethin 20.345..like tht....
21 will be the rqd n...since sum of 20 terms is less thn 590...

Answer 13

Understood?

Answer 14

what are you waiting for? start substituting....

Answer 15

ok

Answer 16

n/2[2a+(n-1)d] > 590 what should i do with this greater sign?

Answer 17

keep it as it is...
put, a, d values, and you'll get a quadratic in n
factorize it.

Answer 18

ok

Answer 19

n/2(2+3n-3)>590

Answer 20

is it right

Answer 21

yes, go ahead and bring it in the form ax^2+bx+c >0

Answer 22

2n+3n^2-3n/2 >590 (can i cross multiply 2)

Answer 23

yes, as 2 is positive, you can cross multiply without any sign change.

Answer 24

3n^2-n-1180>0

Answer 25

and don't you get n+ 3n^2/2 -3n/2 >590

Answer 26

n/2(2+3n-3)>590
n (3n-1) > 590*2
3n^2 -n - 1180 >0
yes, thats correct.

Answer 27

can the middle term break?

Answer 28

or i have to use quadratic formula?

Answer 29

??

Answer 30

apparently, yes. but its hard to see.
i would suggest quadratic formula only..

Answer 31

see, whether u get (x-20) (3x+59) > 0

Answer 32

so can u tell me how is the middle term breaking?

Answer 33

ok got it

Answer 34

1180*3 = 59*60

Answer 35

i solved it by quadratic

Answer 36

you must have got one positive(20 )and one negative solution ?
igone negative.

Answer 37

*ignore

Answer 38

n=20 and n=-59/3

Answer 39

yes, so n-20 is a factor.
n-20 > 0 ---> n>20 ---->n=21

Answer 40

got it ?

Answer 41

yup

Answer 42

thanks

Answer 43

welcome ^_^