For each of the following sequences: @ identify if the sequence is arithmetic, geometric or quadratic’. Justify your response. @ assuming the first it

Yulia 2020-12-17 Answered
For each of the following sequences: @ identify if the sequence is arithmetic, geometric or quadratic’. Justify your response. @ assuming the first item of each sequence is a1, give an expression for aj. (In other words, find a formula for the i-th term in the sequence). @ if the sequence is arithmetic or geometric, compute the sum of the first 10 terms in the sequence i2,12,72,432,2592,...
ii9,18,31,48,69,94,...
iii14,11.5,9,6.5,4,1.5,...
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Expert Answer

l1koV
Answered 2020-12-18 Author has 100 answers

Step 1 The series is 2,12,72,432,2592,... check the ratio 122=6
7212=6
43272=6 this is geometrix series with common ratio r, where r=6 the sequence is geometric (b) the general term ai=a1r(i1) where a1 is the first term , r is the common ratio. substitute the values ai=2(6)(i1) hence, the expression for ai is ai=2(6)i1 Step 2 the sum of first 10 terms is given by the formula a(1rn)1r substitute the values to get the sum of first 10 terms Sn=a(1rn)1r
=2(1(6)n)1(6)
=2(1(6)n)1+6
=17276050 hence, the sum of first 10 terms is given by 17276050

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