Question

Question 15
If sum of the $3^{rd}$ and the $8^{th}$ terms of an AP is 7 and the sum of the $7^{th}$ and ${14}^{th}$ terms is -3, then find the ${10}^{th}$ term.

Answer 1

Let the first term, common difference of an AP are a and d, respectively.
According to the question,
$a_3+a_8=7and{a}_7+a_{14}=-3$
$\Rightarrow a+(3-1)d+a+(8-1)d=7[\because a_n=a+(n-1\left)d\right]$
And a + (7 - 1)d + a + (14 - 1)d = - 3
a + 2d + a + 7d = 7
And a + 6d + a + 13d =-3
2a + 9d = 7 . . . . . . . (i)
And 2a + 19d = - 3 . . . . . . . (ii)
On subtracting eq. (i) from eq.(ii), we get;
$10d=-10\Rightarrow d=-1$
2a + 9 (-1) = 7
$\Rightarrow$ 2a - 9 = 7
$\Rightarrow$ 2a = 16 $\Rightarrow$ a = 8
$\therefore a_{10}=a+(10-1)d$
= 8 + 9(-1)
= 8 - 9 = -1