An arithmetic progression has 10 terms. Sum of the 10 terms is 220. Sum of the odd terms is 100. Find the first term and common difference. pl give me the answer.
maths - Steve Monday, July 17, 2017 at 12:11pm
10/2 (2a+9d) = 220
5/2 (2a+4*2d) = 100
maths - kumar yesterday at 12:10pm
sir,
I get the answer
First term = 18.4 common difference = 4/5
is it correct ?
sorry.its my mistake.
10/2(2a+9d)=220
5 (2a+9d)=220
(2a+9d)=220/5=44..........[1]
5/2(2a+4x2d)=100
2.5(2a+8d)=100
(2a+8d)=100/2.5=40.......[2]
[1]-[2]=d=4
:. 2a+32=40 a=4
That's not what I get. Where's your work?
Did you try actually using your results to see whether they produce the desired AP?
that's better
To solve this problem, we can use the formulas for the sum of an arithmetic progression and the sum of the odd terms in an arithmetic progression.
Let's start with the sum of the 10 terms:
10/2 (2a + 9d) = 220
5(2a + 9d) = 220
10a + 45d = 220
Next, let's use the sum of the odd terms, which includes the first, third, fifth, seventh, and ninth terms:
5/2 (2a + 4d) = 100
10a + 20d = 100
Now we have a system of two equations with two variables (a and d). We can solve this system to find the values of a and d.
To do so, we can multiply the second equation by 2 to eliminate the terms with "d":
20a + 40d = 200
Now we can subtract this equation from the first equation to eliminate the "d" terms:
(10a + 45d) - (20a + 40d) = 220 - 200
10a + 5d = 20
We can solve this equation for "d":
5d = 20 - 10a
d = (20 - 10a) / 5
d = 4 - 2a
Now we can substitute this value of "d" into the second equation:
10a + 20d = 100
10a + 20(4 - 2a) = 100
10a + 80 - 40a = 100
-30a = 20
a = -2/3
Now we can substitute this value of "a" back into the equation we found for "d":
d = 4 - 2a
d = 4 - 2(-2/3)
d = 4 + 4/3
d = 16/3
Therefore, the first term (a) of the arithmetic progression is -2/3 and the common difference (d) is 16/3.
So, the answer you provided, First term = 18.4 and common difference = 4/5, is not correct.