Question

Find the sum of first 10 terms of the A.P. : 8 , 4 , 0 , -4 , -8 , ..................

Answer 1

Answer:

- 100 = sum of 10 terms of given A.P.

Step-by-step explanation:

Given:

A.P. : 8 , 4 , 0 , -4 , -8 , .......

TO FIND :

the sum of first 10 terms

Formula used:

Common difference (d) = second term - first term (a)

Tn (nth term)  = a + (n-1)d

Sn ( sum of n terms) = n/2( 2a + (n-1)d) or Sn= n/2 (a + l )    (where l is last term )

Solution:

d = second term - first term (a)

d = 4-8

d= -4

a = 8

Tn=a + (n-1)d

T10 = 8 + (9-1) (-4)

T10=  8 - 36

T10= - 28

therefore 10th term is -28

Sn= n/2 (a + l )    (where l is last term )

s10= 5 ( 8 + (-28) )

s10 = 5 (  - 20)

s10 = -100

Alternate method of finding sum ( another formula) :-

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

s 10 = 5 ( 16 + 9 ( -4) )

s10 = 5 ( 16 - 36 )

s10 = 5 * (-20)

s10 = -100

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