With !

find the sum of the series:

The sum of the given series  is 130.

Step-by-step explanation:

The sum of series need to be found is .

Apply sum rule,

=.

Apply the constant multiplication rule,

.

.

= 1+2+3+4+5+6+7+8+9+10.

= 55.

=2×55.

=110.

To find ,

Apply sum rule, ,

=2×10.

= 20.

= 110+20.

=130.

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: