AP

The first term of an AP is -11 and its last term is 179. The sum of the whole series is 1680. Calculate 1) the number of terms
2) the sum of all the terms from the 5th to the 11th terms (both inclusive)

Anwser
Find the number of terms n from S = n/2(a + l)

1. From the first line first term a = -11
2. and last term l = 179
3. Sum = n/2 (a + l)
4. 1680 = n/2 (-11 + 179)
5. 1680 = n/2 (168)
6. 1680 = 84 n
7. n = 1680/84
8. n= 20

the sum of all the terms from the 5th to the 11th terms (both inclusive)

Sum of first 11 terms - sum of first 4 terms remember a =-11

Need to get the common difference d

last term 179 is really the 20th term so

20th term = a + (20 - 1) d = 179

-11 + 19d = 179

19d = 190

d = 10

Now you know a = -11 and d = 10

• sum up to 10 terms means n = 10
• sum up to 4 terms means n = 4