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 [tex]a^{18}[/tex]
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 [tex]5^{18}[/tex]
[tex]5^{18}=5^{4+4+4+4+2}=5^{4} \times 5^{4} \times 5^{4} \times 5^{4} \times 5^{2}[/tex]
[tex]\text { since } a^{m+n}=a^{m} \times a^{n}[/tex]
[tex]\begin{array}{l}{=625 \times 625 \times 625 \times 625 \times 25} \\\\ {=390625 \times 390625 \times 25} \\\\ {=152587890625 \times 25} \\\\ {=3814697265625}\end{array}[/tex]
Hence, the value of a^18 is 3814697265625.
