Question

The third term of an arithmetic sequence is -12 and the seventh term is8.What is the sum of the first 10 terms

Answer 1

Answer:

5

Step-by-step explanation:

Given  

The third term of an arithmetic sequence is -12 and the seventh term is 8. What is the sum of the first 10 terms

ANSWER

We know that an = a1 + (n – 1)d

Given n = 3, substituting we get

So a3 = a1 + 2d

Again given a3 = - 12

Substituting we get

 a 1 + 2d = - 12------(1)

Now substituting n = 7 in the above formula we get

a 7 = a1 + 6d

Again substituting a 7 = 8 we get

a 1 + 6d = 8-------(2)

Solving 1 and 2 we get

a 1 + 2d = -12

a1 + 6d = 8

   So subtracting we get

                       4d = 20

                          d = 5

     a1 + 2(5) = - 12

    a 1 = - 12 – 10

    a 1 = - 22

We know that sum to n terms is given by

Sn = n/2 (2a + (n – 1)d) We have n = 10, a = - 22, d = 5

S10 = 10/2 (2(-22) + (10 – 1)5)

S10 = 5(-44 + 45)

S10 = 5

So sum of first 10 terms is 5