Class 10 CBSE | Maths | Term 2 | Arithmetic Progression | Maths Live Class | Exam Winner

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a=2,d=8,sn=90, find n and an.. Can you do this sum with sn=n/2(2a+(n-1)d)

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Yes, I can help you find 'n' and 'an' in the arithmetic sequence where 'a' is 2, 'd' is 8, and 'sn' is 90.
The formula for the nth term of an arithmetic sequence is:
an = a + (n - 1) * d
We are given:
a = 2
d = 8
sn = 90
We need to find 'n' and 'an.' To find 'n,' we can use the formula for the sum of an arithmetic sequence:
sn = (n/2) * [2a + (n - 1) * d]
Substitute the values:
90 = (n/2) * [2 * 2 + (n - 1) * 8]
Now, solve for 'n':
90 = (n/2) * [4 + 8n - 8]
90 = (n/2) * (8n - 4)
90 = 4n^2 - 2n
4n^2 - 2n - 90 = 0
Now, you can solve this quadratic equation for 'n' using the quadratic formula:
n = [-b ± sqrt(b^2 - 4ac)] / (2a)
In this case:
a = 4
b = -2
c = -90
Calculate 'n' using the quadratic formula, and you will get two values for 'n.' Once you have 'n,' you can find 'an' using the first formula I provided.

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