(a) The first term of a geometric sequence is 4, while 2 is the first term...

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(a) The first term of a geometric sequence is 4, while 2 is the first term of an arithmetic sequence. If the common ratio of the geometric sequence equals the common difference of the arithmetic sequence and their third terms are equal, find the common ratio, common difference and the first four terms of both sequences. (b) A geometric progression is given by 2,-1, 1, 1.... Find the general formula in terms of n. (c) The 1st and 10th terms of an arithmetic series are -1 and 10, respectively. Find the sum of the first 10 terms. (d) A geometric sequence, In, is given by In = -3(2)¹-¹. Show that the sum of the first n terms, Sn, is given by Sn=3(1-2). (e) Using mathematical induction, prove that n + 4 < n +9 for all values of nEN. (f) Given the sequence with general term a, 4-5, find i. as ii. a-2 iii. a100 (g) b₁ is a geometric sequence with bsand bg= 4-4. Find the common ratio. (a) The first term of a geometric sequence is 4, while 2 is the first term of an arithmetic sequence. If the common ratio of the geometric sequence equals the common difference of the arithmetic sequence and their third terms are equal, find the common ratio, common difference and the first four terms of both sequences. (b) A geometric progression is given by 2,-1, 1, 1.... Find the general formula in terms of n. (c) The 1st and 10th terms of an arithmetic series are -1 and 10, respectively. Find the sum of the first 10 terms. (d) A geometric sequence, In, is given by In = -3(2)¹-¹. Show that the sum of the first n terms, Sn, is given by Sn=3(1-2). (e) Using mathematical induction, prove that n + 4 < n +9 for all values of nEN. (f) Given the sequence with general term a, 4-5, find i. as ii. a-2 iii. a100 (g) b₁ is a geometric sequence with bsand bg= 4-4. Find the common ratio.

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a Lets take the first term of geometric sequence to be a1 and common ratio to be r Lets take the fir... View the full answer