The sequence is defined by a recursion formula. Write the first four terms of the sequence;
a_1=0; a_n=5a_n-1 +7
what's the problem? Just write them out:
a_1 = 0
a_2 = 5a_1 + 7 = 5*0+7 = 7
a_3 = 5a_2 + 7 = 5*7+7 = 42
and so on
To find the first four terms of the sequence defined by the recursion formula a_1=0 and a_n=5a_n-1+7, we can use the formula to calculate each term one by one.
1. Start by substituting the value of n=1 into the formula:
a_1 = 0
2. Next, use the formula for the second term by substituting n=2 and the previous term (a_1):
a_2 = 5a_1 + 7
= 5(0) + 7
= 7
3. Now, use the formula for the third term by substituting n=3 and the previous term (a_2):
a_3 = 5a_2 + 7
= 5(7) + 7
= 35 + 7
= 42
4. Finally, use the formula for the fourth term by substituting n=4 and the previous term (a_3):
a_4 = 5a_3 + 7
= 5(42) + 7
= 210 + 7
= 217
Therefore, the first four terms of the sequence are: 0, 7, 42, 217.