In a geometric series the first term is 2 and the common ratio is 3.find the number of terms that will give asum of 242

Answer 1

The formula for the sum of a geometric series is given by:

S = a(1 - r^n) / (1 - r)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, we have a = 2 and r = 3. We want to find the value of n that gives a sum of 242.

242 = 2(1 - 3^n) / (1 - 3)

242(1 - 3) = 2(1 - 3^n)

242(-2) = 2 - 6^n

-484 = -4(3^n)

121 = 3^n

Now we need to solve for n. Taking the logarithm of both sides:

log(121) = log(3^n)

2log(11) = nlog(3)

n = 2log(11) / log(3)

Using a calculator, we find that n is approximately 4.5609.

Therefore, the number of terms that will give a sum of 242 is 5.