A geometric progression has a first term of 6 and a common ratio of -3. Find the sixth terms of the progression.
Really?
Surely you must know the critical formulas needed to study this topic
term(6) = a r^5
= 6(-3)^5 = .....
To find the sixth term of a geometric progression with a first term of 6 and a common ratio of -3, we can use the formula for the nth term of a geometric progression, which is given by:
an = a1 * r^(n-1)
Where:
an = nth term
a1 = first term
r = common ratio
n = position of the term in the progression
In this case, the first term (a1) is 6, the common ratio (r) is -3, and we're looking for the sixth term (n = 6). So we can substitute these values into the formula:
a6 = 6 * (-3)^(6-1)
Simplifying this:
a6 = 6 * (-3)^5
Expanding the exponent:
a6 = 6 * (-3 * -3 * -3 * -3 * -3)
Evaluating the expression:
a6 = 6 * 243
a6 = 1458
Therefore, the sixth term of the geometric progression is 1458.
To find the sixth term of the geometric progression, we can use the formula for the nth term of a geometric progression:
\(a_n = a_1 \times r^{(n-1)}\)
In this case, we are given that the first term (a1) is 6 and the common ratio (r) is -3. We need to find the sixth term (a6).
Substituting the given values into the formula, we have:
\(a_6 = 6 \times (-3)^{(6-1)}\)
Now, let's simplify the expression:
\(a_6 = 6 \times (-3)^5\)
According to the rules of exponentiation, \((-3)^5\) means multiplying -3 by itself five times:
\((-3)^5 = -3 \times -3 \times -3 \times -3 \times -3\)
Evaluating the expression, we get:
\((-3)^5 = -243\)
Now, we can substitute this value back into the formula:
\(a_6 = 6 \times (-243)\)
Finally, we can multiply 6 by -243 to find the sixth term:
\(a_6 = -1458\)
Therefore, the sixth term of the geometric progression is -1458.