Math, asked by 1223338, 10 months ago

Answer this question
I will mark the best answer brainliest and will follow both the users


Find the sum of first seventeen terms of an AP whose 4th and 9th terms are - 15 and - 30 respectively​

Answers

Answered by abhagupta7880
1

Answer:

-459 please like and follow me

Attachments:
Answered by intelligentpriya
1

Your question is....

Find the sum of first seventeen terms of an AP whose 4th and 9th terms are - 15 and - 30 respectively....

Your answer is...

Let the first term be common difference and the number of term in an AP are a, d and n....

So, We know that the nth term of an AP....

☞ Tn = a + ( n - 1 ) d.............(i)

•°• 4th term of an AP.....

☞ T4 = a + ( 4 - 1 ) d

☞ T4 = -15 [ Given]

→ a + 3d = - 15.............(ii)

And, 9th term of AP.....

☞ T9 = a + ( 9 - 1 ) d

☞ T9 = -30 [Given]

→ a + 8d = -30.............(iii)

Now, subtract (i) , (ii) , (iii)

Then we get.....

a + 8d = -30

a + 3d = -15

- - +

--------------------

5d = -15

d = -3

Now put the value of D in (i)

Then we get......

☞ a + 3 ( -3 ) => (-15)

☞ a + 3 ( -3 ) => [ a - 9 = -15 ]

☞ a + 3 ( -3 ) => a = -15 + 9

☞ a + 3 ( -3 ) => a = -6

°•° Sum of first n terms of an AP.....

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

Sum of 17 terms of an AP.....

S17 = 17 / 2 [ 2 × ( -6 ) + ( 17 - 1 ) ( -3 ) ]

S17 = 17 / 2 [ -2 + ( 16 ) ( -13 )

S17 = 17 / 2 ( -12 -48 )

S17 = 17 / 2 × ( -60 )

S17 = 17 × ( -30 )

S17 = -510

Hence, The required sum of the first 17 term of an AP is -510....

Hope it helps....(◕ᴗ◕✿)

Please mark me as a brainlist.....

Similar questions