To Find: The value of x, i.e. the last term.
Given: The series and its sum.
The series can be written as x, (x + 3), …, 16, 19, 22, 25
Let there be n terms in the series
25 = x + (n - 1)3
3(n – 1) = 25 – x
x = 25 – 3(n – 1) = 28 – 3n
Let S be the sum of the series
S = n/2[x+25] = 112
⇒ n[28 - 3n + 25] = 224
⇒ n(53 - 3n) = 224
⇒ 3n2 - 53n + 224 = 0
⇒ (n - 7)(n - 32/3) = 0
⇒ n = 7 as n cannot be a fraction.
Therefore, x = 28 - 3n = 28 - 3(7) = 28 - 21 = 7
The value of x is 7.
