SOLUTION: If 30 terms are inserted between 5 and 98 to form an arithmetic sequence, find their sum. i think n is 30 t1 is 5 and tn is 98 but im not sure

Algebra ->  Sequences-and-series -> SOLUTION: If 30 terms are inserted between 5 and 98 to form an arithmetic sequence, find their sum. i think n is 30 t1 is 5 and tn is 98 but im not sure      Log On


   

Question 900070: If 30 terms are inserted between 5 and 98 to form an arithmetic sequence, find their sum.
i think n is 30 t1 is 5 and tn is 98 but im not sure
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
n=32
a1=5
a32=98
S = ½(a1 + an)n
S = ½(5 + 98)*32
S = 16*(103)
S=1648
We can now find "d" even though it wasn't requested
S = ½(2a1 + (n-1)d)n
1648 = ½(2*5 + (31)d)32
1648 = 16(2*5 + 31*d)
1648 = 16(2*5 + 31*d)
103=2*5 + 31*d
103=10 + 31*d
93=31d
d=3
All 32 terms are :
5, 8,11,14,17,20,23,26,29,32,
35,38,41,44,47,50,53,56,59,62,
65,68,71,74,77,80,83,86,89,92,
95,98