The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of geometric sequence with a common ratio of 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric sequence.

Answer 1

Use the formula
a(n) = a + (n-1)*d for the arithmetic series part.
n is the number of the term.
E.g. n = 1 is the 1st term, n = 4 is the 4th term, etc.

72 = a + (21 - 1)d
You can find a in terms of d.
Use that then to get the 1st, 5th and 13th terms in terms of a.

See if you can finish it from there