Science, asked by BrainlyHelper, 1 year ago

If the first two terms of a A. P differ by 4 and eighth term is 25 , then find the Sum of first 20 terms of the A. P

saimeghana1: yuoygfubfyooucljcgjulw6re86

saimeghana1: 700

saimeghana1: ok

Answers

Answered by HappiestWriter012

103

Given , Second term - First term = 4

So, Common difference = d = 4 .

Given that,

Eighth term = 25

We know that Eighth term = a+7d

So , a + 7d = 25

a + 7(4) = 25 .

a = 25 - 28= -3 .

We know that,

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

Now,

Sum of first 20 terms = 20/2 [ 2 (-3)+ (19)4 ] = 10[ -6+76 ] = 700

vipulkarena111p64z4l: 51

saimeghana1: mad

saimeghana1: 51 not 52

saimeghana1: kk

nandini2106: Pradesh plz clear my doubt bro....I think u should take two cases

sapana4: Nandini ,u can only take 4, because by subtracting first term from second ,we get four not -4.

nandini2106: but sapana the question says difference between two terms.....it doesn't tell which term is bigger

sapana4: If minus term is second term or greater than (in number)from first term then,there difference is in minus .But here it is given that ther difference is in positive( means 4) then the biggest term is positive .The smallest term may be negative.

sapana4: Means if first term is 8 and second term is 4 then there difference is -4,because we find d or difference by subtracting first term by second not by subtracting second from the first.If first term is 4 and second term is 8 then d is positive means 4.

nandini2106: hey the question says difference but try to understand that it is in normal language and therefore does not specify whether it is a2-a1 or a1-a2

Answered by agclasher

Thus so

___________________________________________________________@g

SO HERE WE GO

AS IT IS GIVEN THAT THE DIFFERENCE OF THE TWO TWO TERMS OF THE A P IS 4

THEN

A + D - A = 4

. D = 4

SO

. AS 8 TH TERM IS 25

. ➡ A + 7D = 25

. A + 7 ( 4 ) = 25

. A = 25 - 28

. A = - 3

. SO
. AS
.
. S n = n / 2 { 2a + ( n - 1 ) d }

. S 20 = 20 / 2 { 2 ( - 3 ) + ( 20 - 1 ) * 4 }

. = 10 { - 6 + 76 }

. = 10 { 70 }

. = 700

. SO THE SUM OF THE 20 TERMS OF THE A P IS 700

. Hope it helps

. @g here

.

Anny121: well written

agclasher: Oh thxss

Pammi14: very good

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