Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms.
3. Sequence: 2.1, 1.4, 0.7, 0,...
4. Sequence: 1, 1, 2, 3,...
5. Sequence: 0.1, 0.3, 0.9, 2.7,...
Answer (2)
a n = a 1 + ( n − 1 ) d a 1 ; a 2 ; a 3 − f i rs t 3 t er m s o f a r i t hm e t i c se q u e n ce , t h e n a 2 = 2 a 1 + a 3 ======================================== 3. ) a 1 = 2.1 ; a 2 = 1.4 ; a 3 = 0.7 2 a 1 + a 3 = 2 2.1 + 0.7 = 2 2.8 = 1.4 = a 2 O . K . : ) d = a 2 − a 1 → d = 1.4 − 2.1 = − 0.7 a 4 = 0 → a 5 = a 4 + d → a 5 = 0 + ( − 0.7 ) = − 0.7 a 6 = − 0.7 + ( − 0.7 ) = − 1.4 a 7 = − 1.4 + ( − 0.7 ) = − 2.1
4. ) a 1 = 1 ; a 2 = 1 ; a 3 = 2 ; a 4 = 3 2 a 1 + a 3 = 2 1 + 2 = 2 3 = 1 = a 2 − i s n o t an a r i t hm e t i c se q u e n ce
5. ) a 1 = 0.1 ; a 2 = 0.3 ; a 3 = 0.9 ; a 4 = 2.7 2 a 1 + a 3 = 2 0.1 + 0.9 = 2 1 = 0.3 = a 2 − i s n o t an a r i t hm e t i c se q u e n ce
The sequences examined have been determined as follows: the first sequence is arithmetic with a common difference of -0.7 and the next three terms are -0.7, -1.4, -2.1. The second and third sequences are not arithmetic due to inconsistent differences between terms.
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