Question

The first term of an A.P is 5 and it's 100th term Is -292 find the 50th term also find the sum of the 100 terms. ​​

Answer 1

Answer:

146

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Solution:

Sum of first n terms of an A.P is given by

Sn = n/2(2a + (n − 1)d)

Given,

First term (a) = 5, last term (an) = 45 and sum of n terms (Sn) = 400

Now, we know that

an = a + (n – 1)d

⟹ 45 = 5 + (n – 1)d

⟹ 40 = nd – d

⟹ nd – d = 40 …. (1)

Also,

Sn = n/2(2(a) + (n − 1)d)

400 = n/2(2(5) + (n − 1)d)

800 = n (10 + nd – d)

800 = n (10 + 40) [using (1)]

⟹ n = 16

Putting n in (1), we find d

nd – d = 40

16d – d = 40

15d = 40

d = 8/3

Therefore, the common difference of the given A.P. is 8/3.