For the AP: $- 3, - 7, - 11, \dots,$ can we find directly $a_{30} - a_{20}$ without actually finding $a_{30}$ and $a_{20}$ ? Give reasons for your answer.

Open in App

Solution

Step 1: Calculate Common difference
As per the given details
First term, $a = - 3$ .
Common difference,
$d = a_{2} - a_{1}$
$= - 7 - (- 3)$
$= - 4$
Step 2: Calculate the given expression
The difference between any two terms of an AP is proportional to the common difference of that AP,
$∴ a_{30} - a_{20} = a + 29 d - (a + 19 d)$
$= a + 29 d - a - 19 d$
$= 29 d - 19 d$
$= 10 d$
$= 10 (- 4)$
$= - 40$
Hence, the given statement is true, and the value of the given expression is $- 40$ .

Suggest Corrections

Similar questions

For the A.P.: -3,-7,-11,..., can we find $a_{30} - a_{20}$ without actually finding $a_{30} a n d a_{20}$ ? Give reasons for your answer.

- 3, - 7, - 11, . . . . .,

a_{30} - a_{20}

a_{30} and a_{20}

IF $a_{n}$ denotes the nth term of the AP 2, 7, 12, 17, ..., find the value of $(a_{30} - a_{20})$ .

For the AP –3, –7, –11,… can we find directly $a_{30} - a_{20}$ without actually finding $a_{30} a n d a_{20}$ ? Give the reason for your answer.

a_{30} - a_{20}

a_{30} a n d a_{20}

Join BYJU'S Learning Program