Question

A=2,d=8,sn=90then find n and an

Answer 1

Answer:

n = 5,

aₙ = 34

Step-by-step explanation:

$\boxed{\bf Given,} \\\\a=2\\d=8\\S_n=90 \\\\ \boxed{\bf To \ find,} \\\\ n= ? \\a_n=? \\\\ \underline{\bf formula:} \\\\ \boxed{S_n=\frac{n}{2} [2a+(n-1)d]} \\\\ 90=\frac{n}{2}[2(2)+(n-1)(8)] \\\\ 90=\frac{n}{2}[4+8n-8] \\\\ 90\times2=n[8n-4] \\\\ 180=8n^2-4n \\\\ 8n^2-4n-180=0 \\\\4[2n^2-n-45]=0\\\\2n^2-n-45=0 \\\\ 2n^2-10n+9n-45=0 \\\\2n(n-5)+9(n-5)=0 \\\\ (n-5)(2n+9)=0 \\\\ \implies n=5,\frac{-9}{2} \\\\ n \ can't \ be \ negative.\\\\ So,\boxed{n=5} \\\\ \boxed{\bf a_n=a+(n-1)d} \\\\ =>a_n=2+(5-1)(8)$

$a_n=2+4(8) \\\\a_n=2+32\\\\\boxed{a_n=34}$