The 2nd term exists 12 and 7th term exceeds the 4th by 15 exists AP : 7,12,17,....
<h3>
How to estimate the arithmetic progression?</h3>
Given : The second term exists 12th and the 7th term exceeds the 4th term by 15
The formula of the nth term :
![$a_{n}=a+(n-1) d](https://tex.z-dn.net/?f=%24a_%7Bn%7D%3Da%2B%28n-1%29%20d)
Where d exists a common difference
n be the number of terms
a be the first term
Substitute the value of n = 2
![$a_{2}=a+(2-1) d=a+d](https://tex.z-dn.net/?f=%24a_%7B2%7D%3Da%2B%282-1%29%20d%3Da%2Bd)
Let, the second term exists 12
So, a + d = 12 ..........(1)
Substitute the value of n = 7
![$a_{7}=a+(7-1) d=a+6 d](https://tex.z-dn.net/?f=%24a_%7B7%7D%3Da%2B%287-1%29%20d%3Da%2B6%20d)
Substitute n = 4
![$a_{4}=a+(4-1) d=a+3 d](https://tex.z-dn.net/?f=%24a_%7B4%7D%3Da%2B%284-1%29%20d%3Da%2B3%20d)
We are given that the 7th term exceeds the 4th term by 15
So, a+6d-a-3d = 15
3d = 15
d = 5
Substitute the value of d in (1)
So, a+5 = 12
a = 12-5
a = 7
AP : a,a+d,a+2d,.... = 5, 7+5, 7+2(5),....=7,12,17,....
Therefore, AP : 7,12,17,....
To learn more about arithmetic progression refer to:
brainly.com/question/24191546
#SPJ9