To find the common ratio and the first term of the arithmetic progression (AP), we can use the formula for the n-th term of an AP:
\[a_n = a_1 + (n-1)d\]
Given that the second term of the AP is 12:
\[a_2 = a_1 + (2-1)d = a_1 + d = 12\]
Given that the fifth term of the AP is 96:
\[a_5 = a_1 + (5-1)d = a_1 + 4d = 96\]
Now we have two equations:
\[a_1 + d = 12 \quad (1)\]
\[a_1 + 4d = 96 \quad (2)\]
Subtracting equation (1) from equation (2):
\[3d = 84\]
\[d = 28\]
Plugging the value of \(d\) back into equation (1):
\[a_1 + 28 = 12\]
\[a_1 = -16\]
Therefore, the common ratio is 28 and the first term of the AP is -16.
The second term of a Ap is 12 and the fifth term is 96 find the common ratio and the first term
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