1.

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​

Answer»

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


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