Question

Find the sum of the forst 25 terms of a. P whose an=7-3n

Answer 1

Let nth term be the first term :

$a_{n} = 7 - 3n$

$a_{1} = 7 - 3( 1 )$

$a_{1} = 7 - 3$

$a_{1} = 4$

Now, Let n be the 25th term :

$a_{n} = 7 - 3n$

$a_{25} = 7 - 3( 25 )$

$a_{25} = 7 - 75$

$a_{25} = - 68$

Hence,

Sum of 25 terms = $\dfrac{25}{2}[a + a_{25}]$

Sum of 25  terms = $\dfrac{25}{2}[ 4 - 68]$

Sum of 25 terms = $\dfrac{25}{2} [ - 64]$

Sum of 25 terms = 25( - 32 )

Sum of 25 terms = - 800

Thus, sum of 25 terms of the AP is - 800

Answer 2

$a_{n} = 7 - 3n \\ \\ a _{1} = 7 - 3 = 4 \\ a_{25} = 7 - 3 × 25 = 7 - 75 = - 68 \\ \\ S_{n} = \frac{n}{2}( a + a_{n} ) \\ \\ S_{25} = \frac{25}{2}(4 + (-68)) = \frac{25}{2}(-64) = 25 × - 32 = - 800$

Sum of First 25 terms is ( - 800)