Question

The 10th term of an ap is minus 37 and the sum of its first 6 terms is a minus 27 find the sum of first 8 terms

Answer 1

Sum of 1st 8 terms = -76 if The 10th term of an ap is -37 and the sum of its first 6 terms is -27

Step-by-step explanation:

Let say first term of AP = a

common difference = d

10th term of AP = a + 9d  

a + 9d = -37    Eq 1

Sum of 1st 6 Term = -27

6th Term = a + 5d

Sum of 6 term = (6/2)(a + a + 5d)

= 3(2a + 5d)

= 6a + 15d

6a + 15d  = - 27  Eq2

6 * eq1  - eq2

54d - 15d  = -37*6 - (-27)

39d = -222 + 27

=> 39d = -195

=> d =  -5

a + 9d = -37

=> a -45 = -37

=> a = 8

AP is

8   , 3   ,   -2  , -7 , - 12  , -17   , - 22 ,  - 27  , -32 , - 37

8th term = a + 7d  

= 8 - 35

= -27

Sum of 1st 8 terms = (8/2)(8 - 27)

= 4 * -19

= -76

Sum of 1st 8 terms = -76

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