Question

the 7 term of an AP is -4 and it's 13 term is -16 Find the sum of its first 19 terms

Answer 1

Answer:

Step-by-step explanation:

7th term = -4

13th term = -16

In general form,

7th term = a + 6d. = -4 ..........1

13th term = a + 12d = -16 ..........2

Solving 1 and 2,we get,

a + 12d = -16

a + 6d = -4

- - =. +. ......(changing signs)

___________

0 + 6d = -12 .......(a cancels)

d = -12/6

d = -2

Putting value of d in 1

a + 6d = -4

a + 6(-2) = -4

a -12 = -4

a = 12 -4

a = 8

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

S19 = 19/2 [ 2(8) + (19-1)(-2)] ........putting values of a and d

= 19/2 [16 + (18)(-2)]

= 19/2 ( 16 - 36)

= 19/2 ( - 20)

= 19(-10)

S19 = -190

Therefore, the sum of first 19 terms of an AP is -190

HOPE IT HELPS YOU!!

Answer 2

There is your ans ....and now put value of a in 19 term then .... your will come ..... there is not - 16 there is 16 value of a