Question

In an AP: a = 2, d = 8, Sn = 90, find n and an​

Answer 1

Answer:

Given, a=2, d=8, Sn=90

To find, n=? , an=?

n=5, an=34

Answer 2

Step-by-step explanation:

$Sn = \frac{n}{2} (2a + (n - 1)d) \\ 90= \frac{n}{2} (2 \times 2 + (n - 1)8) \\ 90 \times 2 = n(4 + 8n - 8) \\ 180 = n(8n - 4) \\ 180= 8 {n}^{2} - 4n \\ 8 {n}^{2} - 4n - 180 = 0 \\ = 4(2 {n}^{2} - n - 45) = 0 \\ 2 {n}^{2} - n - 45 = 0 \\ 2 {n}^{2} - 10n + 9n - 45 = 0 \\ 2n(n - 5) + 9(n - 5) = 0 \\ (n - 5)(2n + 9) = 0 \\ n - 5 = 0 \: or \: 2n + 9 = 0 \\ n = 5 \: \: or \: \: 2n = - 9 \\ n = 5 \: \: or \: \: n = \frac{ - 9}{2}$

$Tn = a+(n-1)d \\Tn=2+(5-1)8\\Tn=2+(4)8\\Tn=2+32\\Tn=34$