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Chapter 12: Q. 12.10 (page 1167)

Find a general term for the sequence whose first five terms are shown 1, 鈭�4, 9, 鈭�16, 25,...

Short Answer

Expert verified

The general term for the given sequence isan=鈭�1n+1n2

Step by step solution

01

Step 1. Given information

The first five terms are shown 1, 鈭�4, 9, 鈭�16, 25,

02

Step 2. Observing the pattern

n12345...nTerms1鈭�49鈭�1625...Pattern鈭�11+112鈭�11+222鈭�1333鈭�14+142鈭�15+152...鈭�1n+1n2

03

Step 3. Conclusion

The numbers are powers of 2. The signs are alternating, with even nnegative.

Therefore, the general term for the given sequence islocalid="1645103580853" an=鈭�1n+1n2

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Most popular questions from this chapter

Determine if each sequence is arithmetic. If so, indicate the common difference.

a9,20,31,42,53,64,鈥�b12,6,0,-6,-12,-18,鈥�c7,1,10,4,13,7,鈥�

Find the eleventh term of the sequence 7,14,28,56,112,224,鈥�Then find the general term for the sequence.

Find a general term for the sequence whose first five terms are shown. 4, 8, 12, 16, 20, 鈥�

Find the sum.

鈭�6i=1152i

Find the fifth term of(a+b)8
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