Answer:
402
Step-by-step explanation:
The standard formula for the nth term of an arithmetic sequence is:
t + (n - 1)d
where t is the first term and d is the common difference. We can substitute to create a system of equations to solve for the first term and common difference:
22 = t + (5 - 1)d
62 = t + (15 - 1)d
22 = t + 4d
62 = t + 14d
We can use elimination to cancel out t:
62 = t + 14d
-( 22 = t + 4d )
40 = 10d
d = 4
Now, we can substitute the common difference to find the first term:
22 = t + 4*4
22 = t + 16
t = 6
Lastly, we can substitute values in the first equation to find the 100th term:
a100 = t + (n - 1)d
a100 = 6 + (100 - 1)(4)
a100 = 6 + (99)(4)
a100 = 6 + 396
a100 = 402
