Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# The Nth Term of a Sequence is Given by an = 2n2 + N + 1. Show that It is Not an A.P. - Mathematics

The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.

#### Solution

We have:
an = 2n2 + n + 1

$a_1 = 2 \times 1^2 + 1 + 1$

$= 4,$

$a_2 = 2 \times 2^2 + 2 + 1$

$= 11$

$a_3 = 2 \times 3^2 + 3 + 1$

$= 22$

$a_2 - a_1 = 11 - 4$

$= 7$

$\text { and } a_3 - a_2 = 22 - 11$

$= 11$

$\text { Since }, a_2 - a_1 \neq a_3 - a_2$

$\text { Hence, it is not an AP } .$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.1 | Q 8 | Page 4