What is the 32nd term of the arithmetic sequence where a1 = 4 and a6 = 34 ?

Question

What is the 32nd term of the arithmetic sequence where a1 = 4 and a6 = 34 ?
Choose one answer.
A. 182
B. 186
C. 190
D. 194

Answer 1

the answer is C

 

I assumed the pattern is adding due to only two numbers are given

 

from a1 to a6, there are five numbers including a6 (i.e. a2, a3, a4, a5, a6)

 

so 34-4 = 30 and then divided 30/5 = 6

 

therefore a2 = 10, a3 = 16, a4 = 22. a5 = 28,  a6 = 34 and so on.

 

based on that, the formula will be 6(n-1)+4 where n mean the number in a1, a2, a3, etc (i.e. 1, 2, 3, 4)

 

test for a1, n=1 so 6(1-1)+4 = 4

 

for a6 where n = =, so 6(6-1)+4 = 6(5)+4 = 34

 

finally for a32 where n = 32, so 6(32-1)+4 = 6(31)+4 = 186+4 = 190