Question

The average of 10 terms and12 terms of an AP is 12 and14 respectively. 5^th term ofthe progression will be?​

Answer 1

Answer:

11

Step-by-step explanation:

Average of ten terms= 12

Sum of 10 terms =120

120=5(2a+9d)

2a+9d=24---------------------------1

Average of 12 terms =14

sum of 12 terms =168

168=6(2a+11d)

168/6=2a+11d

2a+11d=28--------------------------2

subtract equation 1 from 2

2a + 11d =28

-2a +-9d=-24

-------------------

        2d=4

          d=2

substitute d=2 in equation 1

2a + 9*2= 24

2a+18=24

2a =6

a= 3

a=3          d=2            n=5           an=?

an= a+(n-1)d

   = 3+(5-1)2

   =3+4*2

   =3+8

an=11

Therefore the 5th term of the AP is 11