Question

The 6th term of an Arithmetic Progression is 12 and 8th term is 22. Find its second term and the 16th term.​

Answer 1

Answer:

term difference /position difference =common difference

22-12/8-6=5

6th term-4d=2nd term

12-4*5

12-20 = -8

2nd term = -8

8th term+ 8d= 16th term

22+8*5

22+40 = 62

16th term = 62

Answer 2

Answer:n=6 and tn=12

then tn=a+(n-1)d

12=a+5d

a+5d=12_______(1)

n=8 and tn=22

then tn=a+(n-1)d

22=a+7d

a+7d=22______(2)

sub equation 1and2

a+7d=22

a+5d=12

- - -

_________

2d. = 10

d=10/2

d=5

substitute the value of d=5 in eq 1

a+5d=12

a+5(5)=12

a+25=12

a=12-25

a= -13

now, a= -13 d=5 and n=16

then tn=a+(n-1)d

tn= -13+(16-1)5

= -13+(15)5

= -13+125

tn= 112

therefore 16th term of an ap is 112