Question

If a_1=5a
1
​
=5 and a_n=a_{n-1}+4a
n
​
=a
n−1
​
+4 then find the value of a_4a
4
​
.

Answer 1

Answer:

and a_n=a_{n-1}+4a

Step-by-step explanation:

and a_n=a_{n-1}+4a

Answer 2

Correct Question: If $a_1=5$ and $a_n=a_{n-1}+4$ then find the value of $a_4$.

Answer:

The value of $a_4$ is $17$.

Step-by-step explanation:

Recall the $n^{th}$ term of a sequence,

$a_n=a_1+d(n-1)$

where $a_1=$ the first term, $d=$ common difference two consecutive terms and $n=$ number of terms.

Consider the given terms as follows:

$a_1=5$ . . . . . (1)

$a_n=a_{n-1}+4$ . . . . . (2)

Rewrite expression (2) as follows:

$a_n-a_{n-1} =4$

Notice that the number $4$ is the difference between two consecutive terms, i.e., $(n-1)^{th}$ and $n^{th}$ term.

⇒ common difference, $d=4$

To find: the term $a_4$.

Since $a_n=a_1+d(n-1)$ . . . . . . (3)

Substitute the value $5$ for $a_1$ and $4$ for $d$ in the expression (3) as follows:

⇒ $a_n=5+4(n-1)$

For $4^{th}$ term, substitute the value $n=4$, we get

$a_4=5+4(4-1)$

Simplify as follows:

$a_4=5+4(3)$

    $=5+12$

$a_4=17$

Therefore, the value of $a_4$ is $17$.

#SPJ2