Problem Solving

If the sum of n terms of an A.P. is 3n^2 + 5n and its mth term is 164, find the value of m.

13
23
27
33
39

maihuna wrote:If the sum of n terms of an A.P. is 3n^2 + 5n and its mth term is 164, find the value of m.

13
23
27
33
39

Choose C

dtweah wrote:

maihuna wrote:If the sum of n terms of an A.P. is 3n^2 + 5n and its mth term is 164, find the value of m.

13
23
27
33
39

Choose C

3n2+5n=n/2(2a+(n-1)d)
6n2 +10n=(2a-d)n+n2d

Which means d=6
and 2a-d=10
a=8
8+(m-1)6=164
m=27

maihuna wrote:If the sum of n terms of an A.P. is 3n^2 + 5n and its mth term is 164, find the value of m.

13
23
27
33
39

I am missing something & its getting late for me (gotto go to sleep). Just putting my thoughts.

Sum of n terms => n/2[2a+(n-1)d] = 3n^2+5n

nth term => a+(n-1)d

n - number of terms
a - first term
d - difference between the terms in the AP

mth term => a+(m-1)d = 164

zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz ... Good Night

Givne Sn = 3n^2 + 5n.

S1 = 8 i.e. first term =8.

S2 = 3(4)+5(2) = 22.

So sum of the first 2 terms is 22.
We have first term = 8.
Hence second term = 14.
So common difference d = 14 - 8 = 6.

Now mth term = 8+(m-1)6 = 164

i.e. m-1 =26

i.e m =27