Question

Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = −74
−20.5
−151
−22.75
−144

Answer 1

Hello : the general terme is : an = ap +(n-p)r.....   n, p in N and r in R 
let n=17 and p =1
a17 = a1+(17-1)r
-74 = 38 +16r
16r =-112
r = -7
an = a1 +(n-1)r
a27 =38+26(-7) =−144

Answer 2

Answer:

$a_{27}= -144$

Step-by-step explanation:

$a1=-38 \ and \ a_{17}= -74$

use arithmetic sequence to find the rule for nth term

$a_n= a1+ (n-1)d$ where 'a1' is the first term and d is the difference

first term is 38

$a_17= 38+ (17-1)d$

$-74= 38+ (17-1)d$ , solve for d

$-74= 38+16d$

Subtract 38 from both sides

$-112=16d$, divide both sides by 16

$d= -7$

Now we find 26 term using a1= 38 and d=-7

$a_{27}= 38+ (27-1)(-7)=38+(26)(-7)=-144$

$a_{27}= -144$