The 3th and 9th term of a G.p are 54 and 39.366 respectively find
A
a. 6th term
b. Sum of the 4th and 7th
C.product of 2nd and 5th terms
To find the common ratio (r) of the geometric progression, we can divide the 9th term by the 3rd term.
39.366/54 = 0.727
Now, we can use the common ratio to find the common difference (d) of the arithmetic progression by subtracting the 3rd term from the 2nd term.
54 - (54 * 0.727) = 54 - 39.258 = 14.742
Now that we have the common difference, we can find the first term (a) of the arithmetic progression by subtracting 2 times the common difference from the 3rd term.
54 - 2(14.742) = 54 - 29.484 = 24.516
a. To find the 6th term, we can use the formula for the nth term of an arithmetic progression:
Tn = a + (n - 1)d
T6 = 24.516 + (6 - 1)(14.742)
T6 = 24.516 + 5(14.742)
T6 = 24.516 + 73.71
T6 = 98.226
Therefore, the 6th term is 98.226.
b. To find the sum of the 4th and 7th terms, we can use the formula for the nth term of an arithmetic progression:
Tn = a + (n - 1)d
T4 = 24.516 + (4 - 1)(14.742)
T4 = 24.516 + 3(14.742)
T4 = 24.516 + 44.226
T4 = 68.742
T7 = 24.516 + (7 - 1)(14.742)
T7 = 24.516 + 6(14.742)
T7 = 24.516 + 88.452
T7 = 112.968
The sum of the 4th and 7th terms is 68.742 + 112.968 = 181.71.
c. To find the product of the 2nd and 5th terms, we can use the formula for the nth term of an arithmetic progression:
Tn = a + (n - 1)d
T2 = 24.516 + (2 - 1)(14.742)
T2 = 24.516 + 1(14.742)
T2 = 24.516 + 14.742
T2 = 39.258
T5 = 24.516 + (5 - 1)(14.742)
T5 = 24.516 + 4(14.742)
T5 = 24.516 + 58.968
T5 = 83.484
The product of the 2nd and 5th terms is 39.258 * 83.484 = 3275.816