Question

Hey !!

ARITHMETIC PROGRESSIONS :

Find the sum of first 24 terms of the list of numbers whose nth term is given by an = 3 + 2n

NO COPIED ANSWERS !! ​

Answer 1

$\boxed{\textbf{\large{Step-by-step explanation:}}}$

we have given, the nth term is

tn = 3 + 2n

◻so , the terms of AP (arithmetic progression) are

t ( 1 ) = a = 3 + 2(1)

= 5

t ( 2 ) = 3 + 2 ( 2)

= 3 + 4

= 7

Therefor the common difference

d = t2 - t1 = 7 - 5 = 2

d = 2 , a = 5

◻here, note it that the common difference between two consecutive terms of AP is constant

◻The formula for finding the sum of terms in an AP is

Sn =[( n / 2) ( 2a + ( n - 1) d ) ]

S24 =[ (24 /2 )(( 2 (5) + ( 24 - 1) 2)]

=[( 24/ 2) ( 10 + ( 23 x 2 )) ]

=[( 24 / 2 ) ( 10 + 46 )]

. = 24 x 28

= 672

Therefor the sum of first 24 terms of the list of numbers is

$\boxed{\textbf{\large{672}}}$

Answer 2

Solution:-

Given:-

• nth term = 3 + 2n

To Find:-

• Sum of 24 term = ?

Find:-

Taking [ n = 1 ]

=) a1 = 3 + 2 × 1

=) a1 = 5

Taking [ n = 2 ]

=) a2 = 3 + 2 × 2

=) a2 = 7

Now,

Common Difference = d = a2 - a1

=) d = 7 - 5 = 2

Now,

Sum of nth Term = n/2 [ 2a + ( n - 1 )d ]

=) Sum of 24th Term = 24/2 [ 2 × 5 + ( 24 - 1) 2 ]

=) Sum of 24th Term = 12 [ 10 + 23 × 2 ]

=) Sum of 24th Term = 12 × 56

=) Sum of 24th Term = 672

Hence,

Sum of 24th term of the Given A.P is 672.