Question

Find "am" for an arithmetic progression if sum of "m" terms is given by sm = 2m2 + 5m

Answer 1

Sm=2m2+5m
Sm-1=2(m-1)2+5(m-1)
=2m2+5m-7
am = Sm- Sm-1
Am=7

Answer 2

Answer:

$a_m = 4m+3$

Step-by-step explanation:

Sum of m terms :$S_m = 2m^2 + 5m$

Put m = m-1 for sum of m-1 terms

$S_{m-1} = 2{m-1}^2 + 5{m-1}$

$S_{m-1} = 2(m^2+1^2-2m)+ 5m-5$

$S_{m-1} = 2m^2+2-4m+ 5m-5$

$S_{m-1} = 2m^2+m-3$

Now $a_m = S_m - S_{m-1}$

$a_m = 2m^2 + 5m- (2m^2+m-3)$

$a_m = 2m^2 + 5m- 2m^2-m+3$

$a_m = 4m+3$

Hence  $a_m = 4m+3$