Question

can you please help me with this problem guys​

Answer 1

hi!!

let the first term be

a= 8,

d= common difference,

now,.

the formula for finding the nth term=tn= a+(n-1) ×d

now,.

t8= a+(8-1) ×d

31= a+7d...... (1)

also,

t15= a+14d and

t11= a+10d..

according to the Condition,

t15= t11+16

a+14d= a+10d+16

14d-10d= 16

4d= 16

d= 16/4=4.....(2)

now,

substituting value of d in(1),

31= a+7d

31= a+7(4)

31= a+ 28

31-28= a.

3= a

therefore,

first term = 3

common difference = 4

second term=t2= 3+4= 7

third term= t3= 7+4= 11

fourth term= t4= 11+4= 15

therefore

the AP= 3,7,11,15.......

hope this helps ❤☺✌