Question

if first third and fourth terms are 3 21 and 105 what is the second term

Answer 1

let the second term to be x
3:x::21:105
x*21=105*3
21x=105*3
x=105*3/21
x=15
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Answer 2

to find the second term of the AP, we have to subtract the third term from the fouth term. by doing this, we get the common difference.  we get:
105-321= -216
so -216 is the common difference.
now we know that:
a₃-a₂=d (where d is the common difference)
321-a₂=-216
a₂=321+216
a₂=537.
so the second term of the AP is 537