Question

the 16th term of an AP is three times the 5th term if the 12th term is 20 more than the 7th term find the first term and the common difference.

Answer 1

3(a+4d)
(a+6d)+20

Answer 2

that's my working until now

Answer 3

The general form of an AP series is an = a1 + (n-1)*d
a1 being the first term and d the common difference.
You have a16 = 3*a5 and a12 = 20 + a7
Which translates to:
a1 + 15d = 3*(a1+4d)
a1 + 11d = (a1+6d)+20
Solve the system for a1 and d and you'll get your answer.

Answer 4

That was a good start @Abmon98

Answer 5

Thank you so much for your help :D

Answer 6

Anytime :)