Question

If n th term of an A.P. is 4, common difference is 2 and sum of first n terms is –14,
then find first term and the number of terms.

Answer 1

Answer:

first term = -8

7 terms

Step-by-step explanation:

nth rem =  a + (n-1)d = 4

d = 2

a + 2n -2 = 4

a + 2n = 6

a = 6 - 2n

Sum on n terms = (n/2)(a + nth term) = -14

=> (n/2)(a + 4) = -14

=> (n/2)(6-2n+4) = -14

=> (n/2)(10-2n) = -14

=> 5n - n^2 = -14

=> n^2 -5n - 14 = 0

=> n^2 - 7n + 2n - 14 = 0

=> (n-7)(n+2) = 0

=> n = 7  (as n can not be negative : number of term)

a + 2(7) = 6

a = -8

Answer 2

Answer:

first term = -8

7 terms

Step-by-step explanation:

nth rem =  a + (n-1)d = 4

d = 2

a + 2n -2 = 4

a + 2n = 6

a = 6 - 2n

Sum on n terms = (n/2)(a + nth term) = -14

=> (n/2)(a + 4) = -14

=> (n/2)(6-2n+4) = -14

=> (n/2)(10-2n) = -14

=> 5n - n^2 = -14

=> n^2 -5n - 14 = 0

=> n^2 - 7n + 2n - 14 = 0

=> (n-7)(n+2) = 0

=> n = 7  (as n can not be negative : number of term)

a + 2(7) = 6

a = -8

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