Practice section 2 of 17

Write down the first term, common difference and nth term of each AP: (i) $-3,-8,-13,-18,-23,\ldots$; (ii) $1,2\frac12,4,5\frac12,7,\ldots$.

Find the third and seventh terms of an arithmetic progression with first term $a=2$ and common difference $d=0.5$.

Find the twentieth term of the arithmetic progression $7,13,19,25,\ldots$.

Find the number of terms in the arithmetic progression $57,54,51,\ldots,3$.

The third term of an arithmetic progression is 10 and the tenth term is 24. Find the first term and the common difference.

(a) Suppose $x,y,z$ are three consecutive terms of an AP with common difference $d$. Write an equation relating $x,y,z$. (b) Consider: “Since $u_n=2+3n$, we have $u_1=5,u_2=8,u_3=11$. Then $u_2-u_1=u_3-u_2=3$, a constant, so the sequence is an AP.” Is this argument valid? Why?