THE SUM OF THE 2ND AND 5TH TERMS OF AN A.P IS 42. IF THE DIFFERENCE BETWEEN THE 6TH AND 3RD TERM IS 12, FIND THE: COMMON DIFFERENCE, 1ST TERM, 20TH TERM.
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So, what they have told you is
a+d + a+4d = 42
a+5d - (a+2d) = 12
The 2nd equation makes it clear that d=4
Using that in the first equation, a=11
So, a+19d = 87
D=4,a=11,twenth term=87
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To find the common difference, we can use the information given about the 2nd and 5th terms of the arithmetic progression (AP).
Let's denote the common difference as 'd', and the first term as 'a'. The formula to find the nth term of an AP is:
nth term = a + (n-1)d
Given that the sum of the 2nd and 5th terms is 42, we can set up the following equation:
2nd term + 5th term = a + d + a + 4d = 42
Simplifying the equation, we get:
2a + 5d = 42 ----(1)
We are also given that the difference between the 6th and 3rd terms is 12. We can set up another equation:
6th term - 3rd term = a + 5d - (a + 2d) = 12
Simplifying the equation, we get:
3d = 12
d = 4
So, the common difference is 4.
To find the first term, we can substitute the value of 'd' into equation (1):
2a + 5(4) = 42
2a + 20 = 42
2a = 22
a = 11
Therefore, the first term is 11.
To find the 20th term, we can use the formula for the nth term:
20th term = a + (n-1)d = 11 + (20-1)(4) = 11 + 19(4) = 11 + 76 = 87
Therefore, the 20th term is 87.