You visited us 1 times! Enjoying our articles? Unlock Full Access!

Method of Difference

In an A.P i...

Question

In an $A . P$ if sum of its $n$ first terms is $3 n^{2} + 5 n$ and its $k^{t h}$ term is $164$ , find the value of $k$ .

Open in App

Solution

Given $S_{n} = 5 n^{2} + 11 n$
We use $S_{n - 1} = 5 (n - 1)^{2} + 11 (n - 1)$
$S_{n - 1} = 5 (n^{2} + 1 - 2 n) + 11 n - 11$
$S_{n - 1} = 5 n^{2} - 10 n + 5 + 11 n - 11$
$S_{n - 1} = 5 n^{2} + n - 6$
Now
$T_{n} = S_{n} - S_{n - 1} = 5 n^{2} + 11 n - 5 n^{2} - n + 6$
$[T_{n} = 10 n + 6]$

Suggest Corrections

Similar questions

n

3 n^{2} + 5 n

k^{t h}

164

k

n

{3 n}^{2} + 5 n

m^{t h}

164

m

n

3 n^{2} + 5 n

m^{t h}

164,

m

A . P .

n

\frac{3 n^{2}}{2} + \frac{5 n}{2}

25^{t h}

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

Join BYJU'S Learning Program