Question

Question 7
The sum of the $5^{th}$ and the $7^{th}$ terms of an AP is 52and the ${10}^{th}$ term is 46. Find the AP.

Answer 1

Let the first and common difference of AP are a and d, respectively.
According to the question,
$a_5+a_7=52and{a}_{10}=46$
$\Rightarrow a+(5-1)d+a+(7-1)d=52[\because a_n=a+(n-1\left)d\right]$
And a + (10 - 1)d = 46
$\Rightarrow$ a + 4d + a + 6d = 52
And a+ 9d = 46
$\Rightarrow$ 2a + 10d = 52
And a + 9d = 46
$\Rightarrow$ a + 5d = 26 . . . . . .(i)
a + 9d = 46 . . . . . . .(ii)
On subtracting eq.(i) from eq. (ii), we get;
4d = 20 $\Rightarrow$ d = 5
From eq. (i), a = 26 - 5(5) = 1
So, required AP is a, a + d, a + 2d, a + 3d, . . . . i.e, 1, 1 + 5, 1 + 2(5) , 1 + 3(5), . . . . i.e, 1, 6, 11, 16,....