Question

for the A.P. -5,-3,-1 ... find the difference between its 30th term and 20th term

Answer 1

Answer :

$\large{ \star\:\:\boxed{\bf{a_{30}\:-\:a_{20}\:=\:20}}\:\:\star }$

Explanation :

Given :–

• (-5) , (-3) , (-1) , ... are in A.P.
• where a = (-5) and d = 3

To Find :–

• a₃₀ - a₂₀ (Difference of 30th and 20th term of this A.P.)

Formula Applied :–

• $\boxed{\star\:\:\bf{a_n\:=\:a\:+\:(n\:-\:1)d}\:\:\star}$

Solution :–

We have,

• a = (-5)
• d = 2

Now , we have to find a₃₀ - a₂₀  :-

$\rightarrow\sf{a_{30}\:-\:a_{20}}$

$\rightarrow\sf{(a\:+\:(30\:-\:1)d)\:-\:(a\:+\:(20\:-\:1)d}$

$\rightarrow\sf{[(-5)\:+\:(29\:\times\:2)]\:-\:[(-5)\:+\:(19\:\times\:2)]}$

$\rightarrow\sf{(58\:-\:5)\:-\:(38\:-\:5)}$

$\rightarrow\sf{53\:-\:33}$

$\rightarrow\sf{20}$

∴ The difference of 30th and 20th Term of this A.P. is 20 .