Question

Determine the 2nd and rth term of an A.P. whose 6th term is 12 and 8th term is 22

Answer 1

formula for A.P. is a+(n-1)d
6th term:
t6 = a+5d = 12 ......(1)
8th term:
t8 = a+7d = 22 ......(2)

(1)+(2):
a+5d = 12
a+7d = 22
on changing the symbol (a) get cancelled
remaining,
5d = 12
-7d = -22
on solving this we get,
-2d = -10

=> d = 5
sub, d = 5 in (1)
a+5d = 12
a+5(5) = 12
a+25 = 12
a = 12-25

=> a = -13
now, we got the value of a and d
t2 = a+1d =>a+d
= -13+5
t2 = -8

and I think the second is 4th term
t4 = a+4d
= -13+4(5)
= -13+20
t4 = 7

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