Question

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

Answer 1

Answer:

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

Step-by-step 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

$Sum=\frac{n}{2}(2a+(n-1)\times d)\\\\\implies Sum=\frac{70}{2}(2\times -6+(70-1)\times 3)\\\\\implies Sum=35\times (-12+207)\\\\\implies Sum = 35\times 195\\\\\implies Sum = 6825$

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

Answer 2

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