18. If pth term of an A.P. be q and the qth term be p. Then (p+q)th term is
(a) 0
(b) -1
(c) 1
(d) none of these
Answers
Answer:
option a is correct
t (p + q) = 0
step by step explanation:
☑ pth term of an A.P. be q and the qth term be p.
let,
tp = q
tq = p
we know the formula,
tn = a + (n - 1)d
so, tp = a + ( p - 1)d
q = a + (p - 1 ) d..........(1)
and
tq = a + ( q - 1) d
p = a + (q - 1 ) d ...........(2)
were,
a = 1st term
d = common difference
from 1 and 2 , subtract the equation (2) from (1)
q = a + (p - 1 ) d
p = a + (q - 1 ) d
- - -
____________________
(q - p) = (p - 1)d - (q - 1)d
= dp - d - dq + d
= dp - dq
(q - p) = d ( p - q)
(q - p) / (p - q) = d
- ( - q + p) / ( p - q) =d
- (p - q) / (p - q) = d
d = - 1
☑ put the value of d in equation (1)
q = a + (p - 1 ) d
= a + ( p - 1) (-1)
= a - p + 1
a = q + p - 1
Therefor,
t (p + q) = a + ( (p + q) - 1 ) ( -1)
= q + p -1 - p - q + 1
= 0
Step-by-step explanation:
your answer is in the above attachment
