Question

the common ratio of a g.p is 2.if the 5th term is greater than the first term by 45, find the 5tth term

Answer 1

Is g.p. supposed to mean geometric progression? You should not assume that we know that.

The fifth term will be 2^3 = 8 times the second term

a5 = 8 a2
a5 = a2 + 45
0 = 7 a2 -45
a2 = 45/7
a3 = 90/7
a4 = 180/7
a5 = 360/7

Check: a5 - a2 = 315/7 = 45

Answer 2

U didn't really explain it well . I needed a full and understandable answer.

Answer 3

If the first term of a GP is ‘a’ and the common ratio is r, then the n’th term is: ar^(n − 1).
5th term is greater than 1st term by 45. ar^4 - a = 45.
Substitute r = 2 in the expression.
a*2^4 - a = 45
16a - a = 45
15 a = 45
a = 3
5th term = ar^(5 -1) = 3 * 2^4 = 48

Answer 4

a × r^4 - a = 45
Where a= 2
a × 2^4 - a =45
a × 16 - a =45
16a - a= 45
15a =45
Divide through by 15
a = 3

Tn = ar^n-1
Where n= 5 ;a= 3 ; r= 2
T5 = 3 × 2^5 -1
T5 = 3 × 2^4
T5 = 48

Answer 5

Very good