Let There Be an A.P. with the First Term 'A', Common Difference 'D'. If An A Denotes In Nth Term And Sn The Sum of First N Terms, Find. N and D, If a = 8, An = 62 and Sn = 210 - Mathematics

Let there be an A.P. with the first term 'a', common difference 'd'. If an a denotes in nth term and Sn the sum of first n terms, find.

n and d, if a = 8, an = 62 and Sn = 210

Solution

Here, we have an A.P. whose nth term (an), the sum of first n terms (Sn) and first term (a) are given. We need to find the number of terms (n) and the common difference (d).

Here,

First term (a) = 8

Last term (a_n) = 62

Sum of n terms (Sn) = 210

Now, here the sum of the n terms is given by the formula,

S_n = (n/2)(a + l)

Where a = the first term

l = the last term

So, for the given A.P, on substituting the values in the formula for the sum of terms of an A.P., we get,

210 = (n/2)[8 + 62]

210(2) = n(70)

n = 420/70

n = 6

Also, here we will find the value of d using the formula,

a_n = a + (n -1)d

So, substituting the values in the above mentioned formula

62 = 8 + (6 -1)d

62 - 8 = (5)d

54/5 = d

d = 54/5

Therefore, for the given A.P n = 6 and d = 54/5

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RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 56.5 | Page 53