here's a trick for this.

But first we have to work out the last few terms.

From the sequence we've been given, you should be able to see that each term is 2n where n = 1,2,3,...

So the 68th term = 136, the 69th term = 138, and the 70th term is 140.

So our sum (skipping the middle values) is:

2+4+6+...+136+138+140

Now if you switch that sum around, you get:

140+138+136+...+6+4+2

And if you add those two sums, you get:

(2+140)+(4+138)+(6+136)+...+(136+6)+(1…

= 

142+142+142+...+142+142+142

So that's 70 lots of 142, so we can write the sum = 70 x 142 = 9940.

Now you just have to remember that the question wanted the sum of the 70 terms, and we've just calculated twice that sum because we added the sum to the same sum reversed.

So our sum to answer the question is just:

9940/2 = 4970.