Question

26
How many terms of the A. P:9,17,25, .......
must be taken to give a sum 636?​

Answer 1

Answer:

the answer is 12 terms.

Step-by-step explanation:

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

when you put the values given you will get the quadratic equation 8n square + 10n -1272

you can solve it by quadratic formula or middle term splitting( your choice)

I did it by quadratic formula and I got two values which are 12 and -53/4

since the number of terms in an AP can't be negative and have to be a whole number.

therefore -53/4 is rejected and the answer is 12 no. of terms.

Answer 2

Answer:

We must add the first 12 terms to add upto 636.

Step-by-step explanation:

We have,

A.P = 9, 17, 25,.....

So,

a = 9

d = a2 - a1

= 17 - 9

= 8

Now,

We need the sum to be 636,

We know that,

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

We have,

Sn = 636

So,

636 = (n/2)[2(9) + (n - 1)(8)]

636 × 2 = n(18 + 8n - 8)

1272 = n(8n - 10)

1272 = 8n² - 10n

8n² + 10n - 1272 = 0

an² + bn + c = 0

where a = 8, b = 10, c = (-1272)

Using Quadratic formula,

n = [(-b) ± √(b² - 4ac)]/2a

n = [(-(10)) ± √((10)² - 4(8)(-1272)]/2(8)

n = [(-10) ± √(100 + 40704)]/16

n = [-(10) ± √(40804)]/16

n = [(-10) ± 202]/16

n = (-10 + 202)/16 OR n = (-10 - 202)/16

n = (192/16) OR n = (-212/16)

n = 12 OR n = (-53/4)

We omit n = (-53/4) as (-53/4) can't be number of terms,

So,

n = 12

Hence,

We must add the first 12 terms to add upto 636.

Hope it helped and believing you understood it........All the best