Question

if nth term of a sequence is 3-2n find the sum of 15 term​

Answer 1

The sum of 15 term of the sequence = - 195

Given :

nth term of a sequence is 3 - 2n

To find :

The sum of 15 term of the sequence

Solution :

Step 1 of 2 :

Write down the nth term of the sequence

Here it is given that nth term of a sequence is 3 - 2n

Step 2 of 2 :

Find the sum of 15 terms

Sum of 15 terms

$\displaystyle \sf = \sum\limits_{n = 1}^{15} \: (3 - 2n)$

$\displaystyle \sf = \sum\limits_{n=1}^{15} \: 3 - 2\sum\limits_{n=1}^{15}n$

$\displaystyle \sf = \sum\limits_{n=1}^{15} \: 3 - 2\sum\limits_{n=1}^{15}n$

$\displaystyle \sf = (3 \times 15) - 2 \times \frac{15 \times (15 + 1)}{2}$

$\displaystyle \sf =45 - 240$

$\displaystyle \sf = - 195$