someone please please please help me i have no ideal its due and i dont know it someone smart help math thanks?

Asked By: Trutle
Category: Siemens PLC

Find the 7th term of a geometric sequence with t1=5 and r = -2.
300
320
340
360

Find S7 for the geometric series 2 + -6 + 18 + -54 +…
162
-486
1094
-4374

LG
Posted 6 months ago

tn=t1*r^(n-1), so:
t7=5(-2)^(7-1)=320

To find S7, we use the formula:

Sn=[a1(1-r^n)]/(1-r)

So first we have to find r, which -6/2 = 18/-6 = -3, so r=-3, now we have everything we need, taking a1=2:

S7=[2(1-(-3)^7)]/[1-(-3)] = 1094

Sam
Posted 6 months ago

1) The formula to find the nth term in a geometric sequence is (t1)(r)^(n-1), where t1 is the first term, and r is the common ratio. So in this case, it would be:

(t1)(r)^(n-1)

= (5)(-2)^(7-1)……………………………… Substituting 5 for t1, -2 for r, and 7 for n.

= (5)(-2)^(6)

= (5)(64)

= 320.

2) First, we need to find the common ratio. To find that, divide any number by the number preceding it. Let’s take (-6) and (2). The common ratio r is equal to (-6)/(2) which is equal to (-3). So, r = -3.

The first term, t1, in this case is 2. So, t1 = 2.

Now, plug it into the formula.

(t1)(r)^(n-1)

= (2)(-3)^(7-1)…………………………………. Substituting 2 for t1, (-3) for r, and 7 for n.

= (2)(-3)^(6)

= (2)(729)

= 1458.

Hope this helps

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