Question

How many terms of the AP: 24, 20, 16, ..... must be taken so that the sum may be 72?
Explain the double answer​

Answer 1

Answer:

4

Step-by-step explanation:

a=24 d=20-24=-4

Sn=2a+(n-1)*d

So, 72=n/2(2*24+(n-1)*-4)

72*2=48n-4n²+4n

144=-4n²+52n

4n²-52n+144=0

Divide by 4

n²-13n+36=0

Solve this equation n u will get the values of n as

n=9 or n=4

But if u put n=9 u will not get the value as 72

So... n=4

Answer 2

Given -

AP series

24,20,16...........

a = 24

d = a2 - A1

d = 20-24

d= (-4)

Sn = 72

_____________________

Concept need to find out..

✨ No of terms or N = ???

_____________________

Formula used ...

$\boxed{sn = \frac{n}{2} (2a + (n - 1) \times d)}$

_____________________

Solution...

$sn = \frac{n}{2} (2a + (n - 1) \times d) \\ \\ 72 = \frac{n}{2} (2 \times 24 + (n - 1) \times - 4) \\ \\ 72 \times 2 = n(48 +( - 4n + 4) \: ) \\ \\ 144 = n(48 - 4n + 4) \\ \\ 144 = 48n - 4 {n}^{2} + 4</strong><strong>n</strong><strong> </strong><strong>\\ \\ 144 = </strong><strong>5</strong><strong>2</strong><strong>n - 4 {n}^{2} \\ \\ 14</strong><strong>4</strong><strong> = </strong><strong>5</strong><strong>2</strong><strong>n - 4 {n}^{2} \\ \\ 14</strong><strong>4</strong><strong> - </strong><strong>5</strong><strong>2</strong><strong>n + 4 {n}^{2} = 0 \\ \\ 4 {n }^{2} - </strong><strong>5</strong><strong>2</strong><strong>n + 14</strong><strong>4</strong><strong> = 0 \\ \\ </strong><strong>n²</strong><strong>-</strong><strong>1</strong><strong>3</strong><strong>n</strong><strong>+</strong><strong>3</strong><strong>6</strong><strong>=</strong><strong>0</strong><strong> </strong><strong> </strong><strong> </strong><strong>n²</strong><strong>-</strong><strong>9</strong><strong>n</strong><strong>-</strong><strong>4</strong><strong>n</strong><strong>+</strong><strong>3</strong><strong>6</strong><strong>=</strong><strong>0</strong><strong> \\</strong><strong> </strong><strong>\\ n(n - </strong><strong>9</strong><strong>) - </strong><strong>4</strong><strong>(n - </strong><strong>9</strong><strong>) \\ \\ (n - </strong><strong>4</strong><strong>) \: (n - </strong><strong>9</strong><strong>) \\ \\ n - </strong><strong>4</strong><strong>= 0 \: \: \: \: \: \: n - </strong><strong>9</strong><strong> = 0 \\ \\ \\ n = </strong><strong>4</strong><strong> </strong><strong>\: \: \: \: \: n = </strong><strong>9</strong><strong>\\ </strong><strong> </strong><strong> </strong><strong> n = > </strong><strong>4</strong><strong> \: \: \: \: \: \: \: n = > </strong><strong>9</strong><strong>$

______________________

The number of terms for AP series 24,20,16..............are .

4 or 9....

______________________

Other important formula ....

✨✨an => a+(n-1) d

✨✨an => ( a+l ) if last term given...

______________________

Thanks ✨✨☺️