third term of an AP is p and fourth term of the AP is q find the tenth and the - Maths - Arithmetic Progressions

Question

third term of an AP is p and fourth term of the AP is q find the
tenth and the general term

Amit kumar · Accepted Answer

Any nth term of an AP with first no as 'a' and common
difference 'd' is given by an = a + (n-1)d
Thus difference between 3rd and 4th term = common difference = d
=a4-a3 = q-p
Now a3 = a + (3-1)(q-p) = p
a+ 2q- 2p =p
a= 3p-2q
Thus nth term = (3p-2q) + (n-1) (q-p)
Also 10th term = 3p-2q + 9(q-p) = 7q-6p

third term of an AP is p and fourth term of the AP is q find the tenth and the general term