4).  Find an explicit formula an for the nth term of the geometric sequence whose first term is a1 = 4 such that an + 1 an =  1 10for n ≥ 1. an =   please show step by step .

Q: 2. Find the first 4 terms and the 40th term of the arithmetic sequence: = 67.3 – 4.7n - a1 = a2 = az…

A: To find the terms of the given arithmetic sequence, substitute n=1,2,3,....  in the given nth term…

Q: Find two different explicit formulas for the sequence {1, -2, 3, -4, -5, ⋅ ⋅ ⋅}.

A:

Q: Find the generating function for the sequence 1,−2,4,−8,16,….

A: The general expansion of the binomial (1-x)-1 will be, (1-x)-1=1+x+x2+x3+….

Q: erms a1, a2, 43,., IS deni an = 2", for n 2 1. The sequence B, with terms b1, b2, b3, .., is defined…

A: Given :-  The sequence A , with terms a1 , a2 , a3 , ..... are defined by  an = 2n for n ≥ 1. The…

Q: Find the first 4 terms and the 12th term of the geometric sequence: n а, 3D 1024|

A: We are given the following geometric series.               an=102412n Now,…

Q: Write an explicit formula for the sequence: 6 - 1' 7- T 8 9 - x 10 - * 7' 12 + 1' 18 + 12' 24 + ' 30…

A:

Q: A sequence has a recursive formulatn = tn-1+nº, tị = 5. Determine t3.

A: The given recursive formula of the sequence is: tn=tn-1+n3...(1) And t1=5

Q: 4. Find the value of x so that x+7, -x-1, x+ 13,.. shall form a geometric sequence.

A:

Q: Suppose the sequence goes; 4, 8/3, 16/9, 32/27,... please find the sum of the first 25 even terms

A:

Q: Find the n-th term and the first three terms of the arithmetic sequence having a4 = 93 and a8 = 65.

A:

Q: List the first four terms of each sequence. An = 2n + 6: 8 10 12 14 ,.... bn = (4)" : 4 16 64 256…

A: We can find first four term of the given sequences . Put n=1,2 ,3 ,4 and find four terms of the…