Question

Arithmetic sequence 5,3,1,-1 find a^18

Answer 1

Arithmetic sequence  5, 3, 1, -1 then value of a^18 is 3814697265625.

Solution:

Given, arithmetic sequence is 5, 3, 1, -1

We have to find the value of $a^{18}$  

We know that, first term of any A.P is represented by the letter “a”

So, here in our problem first term a = 5

Then we have to find the value of  $5^{18}$

$5^{18}=5^{4+4+4+4+2}=5^{4} \times 5^{4} \times 5^{4} \times 5^{4} \times 5^{2}$

$\text { since } a^{m+n}=a^{m} \times a^{n}$

$\begin{array}{l}{=625 \times 625 \times 625 \times 625 \times 25} \\\\ {=390625 \times 390625 \times 25} \\\\ {=152587890625 \times 25} \\\\ {=3814697265625}\end{array}$

Hence, the value of a^18 is 3814697265625.