Q. If a1=3 and an+1=(an)2−1 then find the value of a4.Answer:
Identify First Term: Identify the first term in the sequence.The first term a1 is given as 3.
Find Second Term: Use the recursive formula to find the second term a2. The recursive formula is an+1=(an)2−1. Substitute n=1 into the formula to find a2. a2=(a1)2−1=(3)2−1=9−1=8.
Find Third Term: Use the recursive formula to find the third term a3. Substitute n=2 into the formula to find a3. a3=(a2)2−1=(8)2−1=64−1=63.
Find Fourth Term: Use the recursive formula to find the fourth term a4. Substitute n=3 into the formula to find a4. a4=(a3)2−1=(63)2−1=3969−1=3968.