Question

The 35th term of an A. P. is 69. Find the sum of its 69 terms:

Answer 1

you can ask your doubt in comments.. cheers!

Answer 2

The sum of 69 terms is 4761

Step-by-step explanation:

The 35th term of an AP = 69

Hence, to the 35th term in AP, we write it as  

$a_{n}=a_{1}+(n-1) d$

$a_{n} = \text{nth term}$

$a_{1} = \text{first term}$

$n= 35$

d = common difference  

$69=a_{1}+34 d$

To find the sum of the 69 terms, we can use the formula,

$S_{69}=\frac{n}{2}\left(2 a_{1}+(n-1) d\right)$

Now, we get,

$S_{69}=\frac{69}{2}\left(2 a_{1}+(68) d\right)$

$S_{69}=\frac{69}{2}\left(2 a_{1}+(68) d\right)$

$S_{69}=69\left(\frac{2 a_{1}}{2}+\frac{(68) d}{2}\right)$

$S_{69}=69\left(a_{1}+34 d\right)$

We know that, $69=a_{1}+34 \mathrm{d}$

$S_{69}=69 \times 69$

$S_{69}=4761$