Question

the sum of the 5th term and 7th terms of an AP is 52 and the 10th term is 46 .find the AP

Answer 1

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

We know that nth term of AP, = a + (n-1)d

Given,

T₅ + T₇ = 52

a + (5-1)d + a + (7-1)d = 52

a + 4d + a + 6d = 52

2a + 10d = 52

a + 5d=26.........................(i)

Again,

T₁₀ = 46

a + (10-1)d = 46

a + 9d = 46........................(ii)

Now,

Substract eqaution (i) form (ii),

a + 9d - {a + 5d} = 46-26
9d- 5d = 20
4d= 20
d= 5
Putting d= 5 in equation (I)
a + 5*5 = 26
a= 26-25
a= 1
Now,
AP is given as
a , (a+d), (a+2d).........
So,
AP will be ,
1 , 6, 11, 16,...........