Question
Is the given series: $0, -4, -8, -12, ....$ forms an $AP$? If it forms an $AP$, then find the common difference d and write three more terms.
✓
Answer
Here: $a_2- a_1= -4 - 0 = -4$
$a_3- a_2= - 8 + 4 = -4$
$a_4- a_3= -12 + 8 = -4$ , since $a_{k+1}- a_k$_ is same for all values of k
Hence, this is an AP.
The next three terms can be calculated as follows:
$a_5= a + 4d = 0 + 4(- 4) = -16$
$a_6= a + 5d = 0 + 5(- 4) = - 20$
$a_7= a + 6d = 0 + 6(- 4) = - 24$
Thus, the next three terms are:$ -16, -20$ and$ -24$
$a_3- a_2= - 8 + 4 = -4$
$a_4- a_3= -12 + 8 = -4$ , since $a_{k+1}- a_k$_ is same for all values of k
Hence, this is an AP.
The next three terms can be calculated as follows:
$a_5= a + 4d = 0 + 4(- 4) = -16$
$a_6= a + 5d = 0 + 5(- 4) = - 20$
$a_7= a + 6d = 0 + 6(- 4) = - 24$
Thus, the next three terms are:$ -16, -20$ and$ -24$
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