1. 0,5, 10, 15, ... , which term has a value of 640?
2. -11, -7, -3, ... , which term has a value of 789
3. a1 = 34.d = 5,n = 40, an = ?
4. 2, 4, 6, 8, ... ,whuch term has a value of 2288?
5. a1 = 6 an = 50, n = 5,d = ?
6. a1 = 18,d = 6,n = 45, an = ?
7. 4, 10, 16, ... , which term has a value of 808
8. a1 = 2,d = 3,n = 199. an = ?
9. 25, 27, 29, ... , which term has a value of 16667
10. a1 = 12, d = 9.n = 120, an = ?
11. 3, 6, 9, ... , whcih term has a value of 678
12. a1 = 3, an = 263, n = 27, d = ?
13. a1 = 6, d = 2,n = 66, an = ?
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Answer:
from the given set of numbers 5,-10,20,-40,80...it appears like Geometric Sequence and with first term a1=5 and the common ratio r=80−40=−4020=20−10=−105=−2
r=−2
the formula to find the nth term in Geometric Progression is
an=a1⋅rn−1
Use now a1=5 and r=−2 and n=15 in the formula
an=a1⋅rn−1
a15=5⋅(−2)15−1
a15=5⋅(−2)14
a15=5⋅16384
a15=81920 the 15th term
A long check helps after all there are only 15 numbers
5, -10, 20, -40, 80, -160, 320, -640, 1280, -2560, 5120, -10240, 20480, -40960, 81920