Question

in arithmetic series the 7th and 8th term are 16 and 20 respectively find series of AP and its term

Answer 1

tn= a+(n-1)d

Therefore,

Seventh  term t7=a+6d=16...........(1)

similarly,t8=a+7d=20....................(2)

solve (1) and (2)

d=4

Put d=4 in (1)

You get a=-8

The AP is

-8-4+0-4.............

Hope it helps.

Answer 2

Answer-

Given,

$a + 6d = 16 - - - - - (i)$

$a + 7d = 20 - - - - - (ii)$

Subtracting equation (i) from (ii),

$a + 7d = 20 \\ a + 6d = 16 \\ - - - - - - \\ d = 4$

Substituting value of d in (i),


$a + 6d = 16 \\ a = 6d - 16 \\ a = - 8$

Now, a = (-8) and d = 4

So the series will be:

$- 8, - 4,0,4,8,12,16,20,24$