The common difference of anAp is 2 and common ratio of Gp is 3 corresponding terms of the Ap and Gp are added to form a new sequence if the 3rd term of this sequence is 8 and the 1st term is 52 find
- 1st terms of Ap
- 1St terms of Gp
The AP would be
a, a+2, a+4, a+6, ...
The GP would be
A, 3A, 9A, 27A, ...
new sequence:
a+A, a+3A+2, a+9A+4
a+A = 52 ---> a = 52-A
a+9A+4 = 8
52-A + 9A = 4
8A = -48
A = -6 <------- first term of GP
then a = 52+6 = 58 <----- first term of AP
check:
AP would be 58, 60, 62, 64, ....
GP would be -6, -18, -54, ...
new sequence:
58-6, 60-18, 62-54, ..
52, 42, 8,
yup, my answer is correct