Math, asked by minal61, 1 year ago

This my few questions if u know pls help me & thank you!
1) Find tn of the A.P 4,9,14,...
2) The 7™ term of an A.P. is 32 and 13™ term is 62.find the A.P
3) The sum of the three consecutive number in A.P is 21 and their product is 231.find the number.
4) The sum of the first 'n' terms of an A.P is 3n²+5n.find the A.P.,hence find its 16™ term.
5)Find the root of the quadratic equation x²-9=0.
6)Solve 4x²-16+15=0 by completing square method.

Answers

Answered by thinkdifferent

1. a= 4 , d= 5 then tn = a + (n-1)d = 4 + (n-1) 5 = 5n-1 answer 2. t7 = a + (7-1) d => a+ 6d = 32 Now t13 = a+ (13-1)d => a+ 12d = 62 solve the equations and get the answer

minal61: Help me :-(! I subtracting equation from 1&2 so I get 6d=26. Then I divide d=26\6

thinkdifferent: Subtract equ 1 from 2 you will get 6d = 30 => d = 5 put this value In equ 1 we get a = 2 so the AP become 2 , 7 , 12 .....

thinkdifferent: Not 26 it's 30

thinkdifferent: Not 26 it's 30 subtract it properly

minal61: Thank you! But can you help me out by my other questions too?

thinkdifferent: Yes but post them one by one

thinkdifferent: 3) let the nos be ( x-d) , x , ( x+d) now according to question ( x-d) + x+ (x+d) = 21 => 3x = 21 => x=7 now multiplying ( 7 -d) x 7 x (7+d) = 231 => 49 -d^2 = 231/7 now solve it for d

thinkdifferent: Plz mark as best

minal61: But I not have that much points :-( ! So I post its all in ones! Thnx fr ur help..can you be my friend at fb? It will help me to ask u more problem,If you want^^

minal61: My answer coming d²=-16 => -4

Answered by kvnmurty

1)
$a=4,d=5\\\\T_n=a+(n-1)d=4+(n-1)5=5n-1\\\\2)\\a+6d=32,\ \ a+12d=62 \\difference=30=6d=>d=5 \\hence,\ a=2\\\\3)\\ numbers\ are=a-d,a,a+d\\\\sum=3a=21,\ a=7\\product=7(7^2-d^2)=231=7*33\\d=root(16)=4\\\\$

4)
$S_1 = 3*1^2+5*1= 8\\S_2=3*2^2+5*2=22\\\\T1= S_1 = 8\\d = S_2-S1= 14\\\\series = 8, 22, 36 .. = \\\\T_n = 8 + (n-1)14\\$

5)
$x^2 - 9 = 0\\\\x^2 = 9 = 3^2\\\\x = +root(9) or - root(9)\\\\x = +3 or - 3\\\\$

6)
is the given expression 4 x^2 - 16 + 15 ? that is 4 x^2 - 1 = 0 ?
then x^2 = 1/4
x = +1/2 or -1/2

or is it 4 x^2 - 16 x + 15 = 0 ? add and subtract 16 or 4^2
if so (2x - 4)^2 - 16 + 15 = 0
2 x - 4 = + 1 or -1
x = 5/2 or 3/2

kvnmurty: u have - 16 x so divide that by 2 and square root of coefficient of x^2. then you get - 4. so add and subtract 4^2.

kvnmurty: u hav soem thing else ? i go now ? what

minal61: I have lots of question,may I give?

minal61: Thanks :-) all is fine

kvnmurty: tomorrow. do not write so many parts in one question, it becomes too much. are these ur home work ? which class r u in ?

kvnmurty: create questions and send their links on my profile. i will do tomorrow. good night.

minal61: I in 10th class :-) ! Yes its homework...

minal61: Good night SD thanks again^^ ,but how I send link on your profile. & I post many question in ones as I not have points :-( !if you at fb I will send you their!

kvnmurty: write questions on my private messages or profile page. if there is no diagram.. make questions clearly..

minal61: OK! :-)

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