Question

a=2 d=8. Sn=90. an=? ​

Answer 1

Answer:

Sn=n/2[2a+(n-1)d]

90=n/2[2×2+(n-1)×8]

180=n[4+8n-8]

180=8n^2-4n

8n^2-4n-180=0

2n^2-n-45=0

2n^2-10n+9n-45=0

2n(n-5)+9(n-5)=0

(2n+9)(n-5)=0

n=-4.5 or 5

n=5 (accept only natural numbers)

an=2×5

an=10

Answer 2

Step-by-step explanation:

sn=n/2(2a+(n-1)D)

$90 = \frac{n}{2} (2(2) +( n - 1)8)$

$90 = \frac{n}{2} \times 2(2 + (n - 1)4)$

$90 = n(2 + 4n - 4)$

$90 = 4 {n}^{2} - 2n$

$2 {n}^{2} - n - 45 = 0$

$2 {n}^{2} - 10n + 9n - 45 = 0$

$2n(n - 5) + 9(n - 5) = 0$

$n = 5$

an=a+(n-1)D

an=2+4(8)

an=34

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