Question

how to find common ratio with first term, no of terms and sum of series (geometric)

Answer 1

geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,



wherercommon ratio a1first term a2second term a3third term an-1the term before the n th term anthe n th term

The geometric sequence is sometimes called the geometric progression or GP, for short.

For example, the sequence 1, 3, 9, 27, 81 is a geometric sequence. Note that after the first term, the next term is obtained by multiplying the preceding element by 3.

The geometric sequence has its sequence formation: 

To find the nth term of a geometric sequence we use the formula:



wherercommon ratio a1first term an-1the term before the n th term nnumber of terms

Sum of Terms in a Geometric Progression

Finding the sum of terms in a geometric progression is easily obtained by applying the formulas:

nth partial sum of a geometric sequence



sum to infinity



whereSnsum of GP with n terms S∞sum of GP with infinitely many terms a1the first term rcommon ratio nnumber of terms

Answer 2

r= ratio of second term to first term