Find the sum of the first 9 terms in the following geometric series.
do not round your answer.
7+21 +63 +

The sum of first 9 terms of the given sequence = 68887

Step-by-step explanation:

Given sequence:

7+21+63......

The given sequence is a geometric sequence as the successive numbers bear a common ratio.

The ratio can be found out by dividing a number by the number preceding it.

For the given geometric sequence common ratio can be given as:

The sum of a geometric sequence is given by:

      when

and

     when

where, represents sum of terms, representing number of terms and represents common ratio and represents the first term.

Since for the given geometric sequence has a common ratio =3 which is >1, so we will use the first formula for sum to calculate the sum of first 9 terms.

Plugging in the values to find sum of first 9 terms.

∴  

Thus sum of first 9 terms of the given sequence = 68887 (Answer)

equal to

step-by-step explanation:

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.