The fourth term of the arithmetic sequence with a = 3 and d = 7 is 16. True or false?

There are a couple ways you could figure this out.

One is you could just figure out the terms.
a = 3
d = 7

That means the sequence starts with 3 and goes up by 7 each time.
a[1] = 3
a[2] = 3+7 = 10
a[3] = 10+7 = 17
a[4] = 17+7 = 24

So obviously the fourth term of the sequence is NOT 16.

We could also use the general formula for the nth term of an arithmetic sequence. Hopefully you've memorized this:
a[n] = a + d(n - 1)

a : first term (3)
d : common difference (7)
n : number of the term you want (4)

Plug in your values:
a[4] = 3 + 7(4 - 1)
a[4] = 3 + 7(3)
a[4] = 3 + 21
a[4] = 24

Answer:
FALSE

P.S. The answer would be true if you started at 7 and went up by 3 --> 7, 10, 13, 16. So that was obviously how they were trying to trick you.

The 4th term
= a + 3d
= 3 + 3(7)
= 24
≠ 16

The statement is false.

Well,

a1 = a = 3
a2 = a + d = 3 + 7 = 10
......
a4 = 3 + 7*3 = 24 <--- is not 16 !!

therefore, the answer is : False

hope it' ll help !!