Question

the second term of an ap is 2 and the third term exceeds the 13 term 10 find the AP​

Answer 1

$\:\: \underline{\underline{\bf{\large\mathfrak{~~Solution~~}}}}$

let the first term and the difference are a and d respectively....

now ....

a(2)=a+(2-1)d

=>2=a+d

and ....

a(3)=a +(3-1)d

=>a(13)+10=a+2d

=>a+12d+10=a+2d

= >10d=-10

=>d=-1

[a(13)=a+(13-1)d=a+12d]

therefore....a=2-(-1)=3

therefore the series is .....3,2,1,0,-1,-2,-3,-4,......