5 and 15 are the first two terms in a geometric sequence. What is the arithmetic difference between the 11th term and the 13th term?
b 5* 3^13 - 5 * 3^11
d 40 * 3^10
e 3^12 - 3^10
Question regarding arithmetic difference is a - b / 2? or only a - b?
I think the answer choice should be 40 * 3^11. Please do check the source and correct me if I am wrong! Also, the fact that we are calculating the difference of the 13th and the 11th term since this is an increasing GP!
The first term or the a0 = 5 and a1 = 15. For geometric progression, a1 = r * a0 where r is the common term.
Hence, r comes out to be 3.
\(a13 - a11 = a0 * (r^13 - r^11) = 5 * (3^13 - 3^11) = 5 * 3^11 * (9-1) = 40 * 3^11\)
Hence, 40 * 3^11 should be the answer.
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