Question

a=2 d=8 sn=90 = n=?​

Answer 1

Step-by-step explanation:

$\because \: S_n = \frac{n}{2} \{2a + (n - 1)d \} \\ \therefore \: 90 = \frac{n}{2} \{2 \times 2 + (n - 1) \times 8\} \\ \therefore \: 90 = \frac{n}{2} \{4 + (n - 1) \times 8\} \\ \therefore \: 90 = \frac{n}{2} \times 4 \{1 + (n - 1) \times 2\}\\ \therefore \: 90 = 2n \{1 + 2n - 2\} \: \\ \therefore \: \frac{90}{2} = n \{1 + 2n - 2\} \: \\ 45 = n(2n - 1) \\ 2 {n}^{2} - n - 45 = 0 \\ 2 {n}^{2} -10 n + 9n- 45 = 0 \\ 2n(n - 5) + 9(n - 5) = 0 \\ (n - 5)(2n + 9) = 0 \\ n - 5 = 0 \: or \: 2n + 5 = 0 \\ n = 5 \: or \: n \: = - \frac{5}{2} \\ \because \: number \: of \: terms \: of \: an \: ap \\ can \: not \: be \: - ve. \\ \therefore \: n = 5$

Answer 2

Answer:

Sn = (n/2)(2a+(n-1)d)  

90 = (n/2)(4+(n-1)8)  

180 = n(8n-4)  

180 = 8n^2-4n  

8n^2-4n-180 = 0  

n=5  

An = 2+4*8=34