The 1st, 5th, and 13th terms of an arithmetic sequence, with common difference d, are the first three terms of a geometric sequence, with common ratio r. Given that the 1st terms of both sequence is 12, find the value of d and the value of r.

Q: The 5th term of a geometric sequence is 1229 and the 13 th term is 206. Write an equation involving…

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Q: The nth term in a sequence is an. How can you represent the next three terms in the sequence?

A: Given, A sequence with, n th term= an

Q: The second and fifth terms in an arithmetic sequence are 12 and 18 respectively. What is the 100th…

A: Use  an=a1+n-1d  to solve the problem.

Q: For a given geometric sequence, the 10 term, a is equal to 37 and the 14" term, a is equal to -74.…

A: Given,

Q: An arithmetic sequence has first term a and common difference d. It is given that the sum of the…

A: Given Information - The first term of the AP = a Common difference = d Sum of the first four terms…

Q: The first term of an arithmetic sequence is 27, and the sixteenth term is -1. Find the nth term of…

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Q: The middle term of an arithmetic sequence equals 17, the last term = 32, and the fourth term = 11.…

A: Given middle term = 17 Last term = 32 Fourth term = 11 T4 = a+3d = 11 Middle term = T6 = a+5d = 17…