Question

Find the sum of the first 70 terms of the sequence –6, –3, 0, 3, 6, ...

Answer 1

Hello :
-3-(-6) =0-(-3)=3-0=6-3=3 ( arhtmitic sequence r= 3)
Un = U1+(n-1)r
U70 = -6+(70-1)(3)=201
sum = n/2 (U1 +U70)
sum = 70/2(-6+201) = 6825

Answer 2

The sum of first 70 terms of the given sequence = 6825

Explanation:

The sequence is given to be : -6, -3, 0, 3, 6, .......

Since, The common difference is same for all the terms in the sequence , so the given sequence is in A.P.

Now, finding the sum of first 70 terms of an A.P.

First term, a = -6

Number of terms, n = 70

Common difference, d = 3

`Sum=(n)/(2)(2a+(n-1)* d)\\\\\implies Sum=(70)/(2)(2* -6+(70-1)* 3)\\\\\implies Sum=35* (-12+207)\\\\\implies Sum = 35* 195\\\\\implies Sum = 6825`

Therefore, the sum of first 70 terms of the given sequence = 6825