the bin term ef an AP lag

1.	the bin term ef an AP lag
Answer» Let a and d be the first term and common difference of the AP. given, pth term of the AP = q and qth term of the AP = p. To show: (p+q)th term is zero. a + (q-1)d = p ------- (1)a + (p-1)d = q ------- (2) Subtract (1) from (2) (p-1)d-(q-1)d = q-p=> (p-q)d = q-p => d = -1 ----- (3) Using (1) and (3) we get, a + (q-1)(-1) = p=> a = p+q-1 -----(4) (p+q)th term = a + (p+q-1)(d) = (p+q-1) + (p+q-1)(-1) {from eq. 3 and 4}(p+q)th term = 0 Hence showed.

Answer»

Let a and d be the first term and common difference of the AP.

given, pth term of the AP = q and qth term of the AP = p.

To show: (p+q)th term is zero.

a + (q-1)d = p ------- (1)a + (p-1)d = q ------- (2)

Subtract (1) from (2)

(p-1)d-(q-1)d = q-p=> (p-q)d = q-p => d = -1 ----- (3)

Using (1) and (3) we get,

a + (q-1)(-1) = p=> a = p+q-1 -----(4)

(p+q)th term = a + (p+q-1)(d) = (p+q-1) + (p+q-1)(-1) {from eq. 3 and 4}(p+q)th term = 0 Hence showed.

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