Question

(2. How many consecutive odd integers beginning with 5 will sum to 480?
3.
Find the sum of first 28 terms of an A.P. whose nth term is 4n - 3.​

Answer 1

Answer:

1) There are 20 consecutive odd integers beginning with 5 will sum to 480.

2) The sum of first 28 terms of an A.P. is 1540.

Explanation:

1) To find : How many consecutive odd integers beginning with 5 will sum to 480?

Solution :

Series of Odd number form an AP.

Where, first term is a = 5

common difference, d = 2

Sum of n term, $S_n=480$

Formula of sum of an A.P is

$S_n=\frac{n}{2}(2a+(n-1)d)$

Substitute the value in the formula,

$480=\frac{n}{2}(2(5)+(n-1)2)$

$480=\frac{n}{2}(10+2n-2)$

$480=\frac{n}{2}(8+2n)$

$480=n(4+n)$

$480=4n+n^2$

$n^2+4n-480=0$

$n^2+24n-20n-480=0$

$n(n+24)-20(n+24)=0$

$(n+24)(n-20)=0$

$n=-24,20$

Reject n=-24.

Accept n=20

Therefore, There are 20 consecutive odd integers beginning with 5 will sum to 480.

2) To find : The sum of first 28 terms of an A.P. whose nth term is 4n-3.​

Solution :

The nth term is $a_n=4n-3$

The first term is $a_1=4(1)-3$

$a_1=1$

The second term is $a_2=4(2)-3$

$a_2=5$

The common difference is  

$d=a_2-a_1$

$d=5-1$

$d=4$

The sum of the first 28 term is

$S_{28}=\frac{28}{2}(2(1)+(28-1)4)$

$S_{28}=14(2+(27)4)$

$S_{28}=14(2+108)$

$S_{28}=14(110)$

$S_{28}=1540$

Therefore, The sum of first 28 terms of an A.P. is 1540.

Answer 2

Answer:

1540

Explanation:

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