If (a=15) and (d=-4), what will be the third term?

(7)

In an arithmetic progression, the first term is \\(a\\), and each later term is obtained by repeatedly adding the common difference \\(d\\). Thus the second term is \\(a+d\\), while the third term is \\(a+2d\\). A negative common difference means that the repeated additions make the terms smaller.

Here \\(a=15\\) and \\(d=-4\\). The first term is 15, the second is \\(15+(-4)=11\\), and the third is \\(11+(-4)=7\\). Equivalently, the third-term formula gives \\(a_3=a+2d=15+2(-4)=15-8=7\\). Therefore choice B is correct. The value 11 is the second term, not the requested third term.

This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..