Question

urgent!!!

Question no. 15 please ​

Answer 1

Step-by-step explanation:

Let A be the first term and D the common difference of the given A.P.

$\[ \begin{array}{l} \tt T_{p}=A+(p-1) D =a \\ \\ \tt T_{q}=A+(q-1) D=b \\ \\ \tt T_{r}=A+(r-1) D=c \\ \\ \tt\therefore(i) \times(q-r)+(i i) \times(r-p)+(i i i) \times(p-q) \\ \\ \tt \Rightarrow A[(q-r)+(r-p)+(p-q)]+D[(p-1)(q-r)+(q-1)(r-p)+(r-1)(p-q)] = a(q - r) + b(r - p) + c(p - q )\\ \\ \tt \Rightarrow A[0]+D[p q-q-p r+r+q r-r-p q+p+p r-p-q r+q]=a(q-r)+b(r-p)+c(p-q) \\ \\ \tt \Rightarrow a(q-r)+b(r-p)+c(p-q)=A \times 0+D \times 0=0 . \end{array} \]$