Question

if the 4th term of an AP is 11 and 10th term is 16 then what will be the first term of this AP ?​

Answer 1

Answer:

The common difference is $\frac{5}{6}$

Step-by-step explanation:

Let a be the first term d be the common difference of the A.P.

Given $a_4=11,a_{10}=16$

We know that $a_n=a+(n-1)d$

Thus $a_4=11\Rightarrow a+(4-1)d=11\Rightarrow a+3d=11...(1)$

and $a_{10}=16\Rightarrow a+9d=16...(2)$

Subtract (1) from (2)

$\Rightarrow a+9d-(a+3d)=16-11\\\Rightarrow 6d=5\Rightarrow d=\frac{5}{6}$