Question

The 18th term of an arithmetic sequence with common difference 4 is 23.What is its 23rd term​

Answer 1

Answer :

$\large{\dag\:\boxed{\star\:\:a_{23}\:=\:43\:\:\star}\:\dag}$

Explanation :

Given :–

• a₁₈ = 23 (18th Term is 23.)

• d = 4 (Common Difference is 4. )

To Find :–

• a₂₃ (23rd Term of this A.P.)

Formula Applied :–

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

Solution :–

We have a₁₈ = 23 and d = 4 .

$\rightarrow\sf{a_{18}\:=\:23}$

$\rightarrow\sf{a_{18}\:=\:a\:+\:(18\:-\:1)d}$

$\rightarrow\sf{23\:=\:a\:+\:(17\:\times\:4)}$

$\rightarrow\sf{23\:=\:a\:+\:68}$

$\rightarrow\sf{a\:=\:23\:-\:68}$

$\rightarrow\bf{a\:=\:(-45)}$

Now , we have , a = (-45) , d = 4  and n = 23 .

Putting these values in the Formula :

$\rightarrow\sf{a_n\:=\:a\:+\:(n\:-\:1)d}$

$\rightarrow\sf{a_{23}\:=\:(-45)\:+\:(23\:-\:1)(4)}$

$\rightarrow\sf{a_{23}\:=\:(-45)\:+\:(22\:\times\:4)}$

$\rightarrow\sf{a_{23}\:=\:(-45)\:+\:88}$

$\rightarrow\boxed{\bf{a_{23}\:=\:43}}$

∴ 23rd Term of this A.P. is 43 .