Find the sum of the following arithmetic progression: 1) 50, 46, 42,...to 10 terms 2) 1,3,5,7,...to 12 terms 3) 3 ,9/2, 6,15/2,...to 25 terms 4) a + b, a-b, a-3b, ...22 terms 5) −/+,3−2/+,5−3/+,...to n terms 6) -26, -24, -22,...to 36 terms. 7) 5,2,-1,-4,-7,.... to n terms
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Answer:
Find:
(i) 10th term of the A.P. 1, 4, 7, 10, ...
(ii) 18th term of the A.P.
√
2
, 3
√
2
, 5
√
2
, ...
(iii) nth term of the A.P. 13, 8, 3, −2, ...
ANSWER:
(i) 1, 4, 7, 10...
We have:
a = 1
d = 4-1 = 3
a10 =a+(10-1)d [an=a+(n-1)d] = a +9d = 1+9×3 = 28
(ii)
√
2
, 3
√
2
, 5
√
2
...
We have:
a =
√
2
d = 3
√
2
-
√
2
= 2
√
2
a18 = a+(18-1)d [an=a+(n-1)d] = a+17d =
√
2
+17(2
√
2
) =
√
2
+34
√
2
= 35
√
2
(iii) 13, 8, 3, −2...
We have:
a = 13d = 8 -13 = -5
an = a+(n-1)d = 13+(n-1)(-5) = 13-5n
Step-by-step explanation:
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