SOLUTION: sequence 4,12,.....972 can this be arithmetic, if so what is equation for nth term and what term number is 972 can this be geometric, if so what is equation for nth term and

If so then d = 12-4 = 8, a1 = 4

an = a1+(n-1)d

We see if 972 can be = an for some natural number n

972 = 4 + (n-1)(8)
972 = 4 + 8n - 8
972 = 8n - 4
976 = 8n
122 = n

Yes, since 122 is a natural number, and 972 is term number 122.

So

an = a1+(n-1)d  becomes

an = 4+(n-1)8 = 4+8n-8 = 8n-4

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If so then r = 12/4 = 3, a1 = 4

an = a1rn-1

We see if 972 can be = an for some natural number n

972 = 4·3n-1
Divide both sides by 4

243 = 3n-1

We can break 243 as 35

35 = sn-1

So the exponents of 3 must be equal:

5 = n-1`

6 = n

Yes, since 6 is a natural number.  In fact since 6 isn't so large,
we can write the sequence to 6 terms, though it isn't necessary,
it's just a check:

4, 12, 36, 108, 324, 972

So 972 really is term number 6.

an = a1rn-1  becomes

an = 4·3n-1

Edwin