The sum of the 1st 4 terms of an AP is 216 and the sum of the 1st 18 terms is 988. What is the first term.

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The sum of the first n terms of an arithmetic progression with first term a and common difference d is `S_n = (n/2)*(2a + (n - 1)*d)`

Here, S4 = 2*(2a + 3d) = 216 and S18 = 9*(2a + 17d) = 988

=> 2a + 3d = 108 and 2a + 17d = 988/9

=> 34a + 51d = 1836 and 6a + 51d = 988/3

Subtract the two equations

=> 34a - 6a = 1836 - 988/3

=> 28a = 4520/3

=> a = 1130/21

The first term of the series is 1130/21

akshaygoel96 | Student, Grade 11 | (Level 1) Honors

Posted on

SO FIRst of all
t4 = a +(n-1)d
216= a +(4-1)d
216 = a + 3d
so now solve for "a"
you get
a = 216 - 3d

now second case

t18 = a +(18-1)d
988= a+ 17d

now subsitute the value of a as you found above ,
988 = 216-3d +17d .... 988-216 =14d
solve for d
d= 55.14

now plug the vALUE OF "d" in one equation (which one you like)
you will get a = 51 , means the first term :)