Write the first five terms of the sequence and obtain the corresp… - Vidyadip

Question

Write the first five terms of the sequence and obtain the corresponding series $a_1 = a_2 = 2, a_n = a_{n-1} - 1, n > 2.$

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Answer

Given: $a_1 = a_2 = 2, a_n = a_{n-1} - 1, n > 2$
Putting $n = 3, 4$ and $5,$ we get
$a_3 = a_{3-1} - 1 = a_2{- 1} = 2 - 1 = 1$
$a_4 = a_{4-1} - 1 = a_3{- 1} = 1 - 1 = 0$
$a_5 = a_{5-1} - 1 = a_4{- 1} = 0 - 1 = -1$
Hence the first five terms are $2, 2, 1, 0, -1.$
Therefore, corresponding series is $2 + 2 + 1 + 0 + (-1) + .......$

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