Class 11

Math

Algebra

Sequences and Series

The sum of three A.M. between $2,10$ is :

- $18$
- $16$
- $17$
- $15$

such that $2,A_{1},A_{2},A_{3},10$ are in A.P.

$a_{n}=1+(n−1)d$

$n=3+2=5,a=2$

$∴10=2+(5−1)d$

$∴4d=8$

$n=3+2=5,a=2$

$∴10=2+(5−1)d$

$∴4d=8$

$∴d=2$

$A_{1}=a+d=2+2=4$

$A_{2}=a+2d=2+4=6$

$A_{3}=a+3d=2+6=8$

$∴$ Sum of $4+6+8=18$

$A_{1}=a+d=2+2=4$

$A_{2}=a+2d=2+4=6$

$A_{3}=a+3d=2+6=8$

$∴$ Sum of $4+6+8=18$