Class 10

Math

All topics

Arithmetic Progressions

Is the following sequence an $AP$? If true, find the common difference $d$ and write three more terms.

$0,−4,−8,−12,$$⇒$ Difference between second and first term $=−4−0=−4$

$⇒$ Difference between third and second term $=−8−(−4)=−8+4=−4$

$⇒$ Difference between fourth and third term $=−12−(−8)=−12+8=−4$

$⇒$ Since, difference is same, it is an $A.P$

$⇒$ Common difference $=d=−4$

$⇒$ We have to find next three terms. We are given $4$ terms.

$⇒$ We have to find $5_{th},6_{th}$ and $7_{th}$ terms.

$⇒$ $5_{th}$ term $=4_{th}term+d=−12+(−4)=−16$

$⇒$ $6_{th}$ term $=5_{th}term+d=−16+(−4)=−20$

$⇒$ $7_{th}$ term $=6_{th}term+d=−20+(−4)=−24$

Hence $5_{th},6_{th}$ and $7_{th}$ terms are $−16,−20,−24$