Question

Find the sum of the series 5+7+9+10+13+13+17+16+.....to60 terms

Answer 1

Okay! So, we know that the first term of the series is 5.
So, take a = 5.
We know that d = a2 - a
                          = 7 - 5 = 2

We know that an = a+(n-1)d
So, 
a60 = 5+59*2
       = 5+118
       = 123

We have to find the sum of 60 terms (i.e, S60)

We know that Sn = n/2(a+an)
So,
S60 = 60/2(5+123)
       = 60/2*128
       = 60*64 [ As 128/2 = 64 ]
       = 3840

Thus, the sum of 60 terms is 3840.

Answer 2

Answer:

6870

Step-by-step explanation:

This following series is not in an AP, hence we can turn it into an ap by adding two terms consecutively, i.e- 5+7=>12 & 9+10+>19. By adding these terms we get two numbers 12 and 19, the difference between them being 7. If we do the same procedure for two other pair of terms in this series say 13,13 & 17,16 we get 26 and 33 difference between them again being 7 hence we have sucessfully created a new ap with first term (a) = 12 and common difference (d)= 7, then we can substiture these values in the sum of n terms formula to get:

=> n/2 * (2a+(n-1)d)

=> 30/2 * (2*13+(30-1)7)

=> 15 * (26+29*7)

=> 30 * (26+203)

=> 30 * 229 = 6870

Note: The no of terms becomes 30 as after succesively adding two pairs of terms the no of terms will become half of the original