# Write down in terms of n, an expression for the nth termof the following sequences:a) 4, 1, - 2, -5, -8 b) -7, -12, -17, -22, -27?

$\begin{array}{l}\text{Given sequence},\\ \left(a\right)4,\ 1\ ,\ -2,\ -5,\ -8\\ \text{This is an AP,}\ a=4,\ d=\left(1\right)-\left(4\right)=-3\\ T_n=a+\left(n-1\right)d=4+\left(n-1\right)\cdot-3=7-3n\\ \left(b\right)-7,\ -12,\ -17,\ -22,\ \ -27\\ \text{This is an AP, }a==-7,\ d=\left(-12\right)-\left(-7\right)=-5\\ T_n=a+\left(n-1\right)d=-7+\left(n-1\right)\cdot-5=-2-5n\end{array}$

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