Question

what is the value of a1 for a geometic sequence with a4=40 and a6=160?

Answer 1

'r' is the common ratio.
a is the first value in the sequence.

a4 = a*(r^3) = 40
a6 = a*(r^5) = 160

Find that little guy, a. He's hiding in there.

Answer 2

haha

Answer 3

The general geometric Progression is given as by making use of a4 and a6 value we find r value.
\[\frac{a6 = ar^6-1}{a4 = ar^4-1}\]
\[\frac{160 = ar^5}{40 = ar^3}\]
\[\frac{160 = r^5}{40 = r^3}\]
4 = r5-3
4 = r2
take square root on both side
√4 = √ r2
2 = r...........(1)
use the value of r to find a.
a4=a∗(2)4−1
40 = a23
40 = a 8
40/8 = a
5 = a.........(2)
a1 = a∗(2)4−1
= 5 *2(1-1)
= 5*20
=5*1
= 5
the value of a1 is 5.

maths question paper for class 9 ICSE - http://icse.edurite.com/icse-question-papers/icse-maths-question-papers-for-class-9.html