Question

if 16th term of AP is 5 times of third term if 10th term is 41 then find the sum of its 15th term ??

Step By Step Explanation...
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Answer 1

Given:

16th term = a + 15d

3rd term = a + 2d

5(a + 2d) = a + 15d

5a + 10d = a + 15d

4a - 5d = 0

4a = 5d

a = 5d/4

Also,

10th term = a + 9d = 41

a = 5d/4

so,

5d/4 + 9d = 41

5d/4 + 36d/4 = 41

5d + 36d/4 = 41

41d/4 = 41

41d = 164

d = 164/41

d = 4

a + 9d = 41

a + 36 =41

a = 5

Now,

n = 15

a = 5

d = 4

Sn = n/2(2a + (n-1)d)

= 15/2 (10 + 14 * 4)

= 15/2*66

= 495

Answer 2

Refers to attachment ♡~