Question

If the first term of an Ap is -18 and its
10th term is zero, then find its common
difference
​

Answer 1

Given :

• First term of the AP = - 18

• 10th term of the AP = 0

To find :

The common difference of the AP.

Solution :

Let the common difference of the AP be d .

Here ,

• The nth term of the AP will be 10 term of the AP (i.e, 0)

• The number of terms (n) of the AP will be 10

Since , we are provided with the nth term , first term and no. of terms of the AP , hence we can use the Equation for nth term of the AP and by using it , we can find the required value.

Formula for nth term of an AP :

$\boxed{\bf{t_{n} = a_{1} + (n - 1)d}}$

Where :

• tn = nth term
• a1 = First term
• n = No. of terms
• d = Common Difference

$:\implies \bf{t_{n} = a_{1} + (n - 1)d}$

$:\implies \bf{0 = (-18) + (10 - 1)d}$

$:\implies \bf{0 = (-18) + 9d}$

$:\implies \bf{-(-18) = 9d}$

$:\implies \bf{18 = 9d}$

$:\implies \bf{\dfrac{18}{9} = d}$

$:\implies \bf{2 = d}$

$\underline{\boxed{\therefore \bf{2 = d}}}$

Hence, the common difference of the AP is 2 .