solve the equation 2+5+8 +x=155 - Maths - Sequences and Series

Question

solve the equation 2+5+8 +x=155

Shridhar Kaushik · Accepted Answer

We have, $2 + 5 + 8 + + x = 155$ L H S of this equation represent an A P with a = 2 and d = 3 We know that, $S_{n} = \frac{n}{2} {2 a + (n - 1) d} \Rightarrow 155 = \frac{n}{2} {4 + (n - 1) \times 3} \Rightarrow 310 = n (3 n + 1) \Rightarrow 3 n^{2} + n - 310 = 0 \Rightarrow 3 n^{2} + 31 n - 30 n - 310 = 0 \Rightarrow n (3 n + 31) - 10 (3 n + 31) = 0 \Rightarrow (3 n + 31) (n - 10) = 0 \Rightarrow n = 10 or \frac{- 31}{3}$ But n can not be negative âˆ´ n = 10 Now, an = a + (n â€“ 1) d $\Rightarrow a_{10} = 2 + (9) \times 3 \Rightarrow a_{10} = 29$ Hence x = 29

solve the equation 2+5+8...+x=155