The sum of all terms of the AP: -4, -1, 2, 5, x is 437 - Maths - Arithmetic Progressions

Question

The sum of all terms of the AP: -4, -1, 2, 5, x is 437 Find
x

ramandeep.singh · Accepted Answer

First term, a = -4 Common difference, d = 3 Sn = 437 $\Rightarrow \frac{n}{2} [2 a + (n - 1) d] = 437 \Rightarrow \frac{n}{2} [2 (- 4) + (n - 1) (3)] = 437 \Rightarrow n [3 n - 11] = 874 \Rightarrow 3 n^{2} - 11 n - 874 = 0 \Rightarrow 3 n^{2} - 57 n + 46 n - 874 = 0 \Rightarrow (3 n + 46) (n - 19) = 0 ∴ 3 n + 46 = 0 o r n - 19 = 0 \Rightarrow n = \frac{- 46}{3} o r n = 19$ As number of terms can not be negative, âˆ´n = 19 $∴ a_{19} = a + (19 - 1) d = a + 18 d = - 4 + 18 (3) = 50$ Hope you get it Cheers!

The sum of all terms of the AP: -4, -1, 2, 5,.....x is 437. Find x.