Question

Find the sum of the first 25 terms of an A.P. who's n^th term is given by 7-3n

Answer 1

Step-by-step explanation:

Given:-

$\bf a_n = 7-3n, n = 25$

To find:-

$\bf S_{25} \: = \: ? \:$

Solution:-

First find the value of 'a' and 'd'

$\large\sf a_1= 7-3n=7-3×1= 4$

$\large\sf a_2= 7-3×2= 1$

$\large\sf a_3= 7-3×3= -2$

Now,

$‎ ‎ ‎‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎\large\sf d = a_2-a_1= 1 - 4 = - 3$

We know that,

$\large\red{\boxed{ \mathtt\color{darkblue}{Sum \: of \: n \: terms \: of \: A•P = \frac{n}{2} (a + a_n)}}}$

$\sf\large \: \: = \frac{25}{2} (4+7 - 3n)$

$\sf\large \: \: = \frac{25}{2} (11 - 3 \times25 )$

$\sf\large \: \: = \frac{25}{2} (11 - 75)$

$\sf\large \: \: = \frac{25}{\cancel2} \times (\cancel{64})$

$\sf\large \: \: = 25 \times 32$

$\large\bf = \: - 800$

$\bf\therefore \underline{Sum \: of \: 25 \: term \: of \: an \: } \\ \bf \underline{A.P \: is \: - 800}$

Answer 2

Answer:

Input parameters & values: The number series 2, 4, 6, 8, 10, 12, . . . . , 50. Therefore, 650 is the sum of first 25 even numbers.