# Let There Be an A.P. with the First Term ‘A’, Common Difference’. If a Denotes Its Nth Term and Sn the Sum of First N Terms, Find N And Sn, If A = 5, D = 3 And An = 50. - Mathematics

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

n and Sn, if a = 5, d = 3 and an = 50.

#### Solution

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

Here,

First term (a) = 5

Last term (a_n) = 50

Common difference (d) = 3

So here we will find the value of n using the formula, a_n = a + (n -1)d

So, substituting the values in the above-mentioned formula

50 = 5 + (n -1)3

50 = 5 = 3n - 3

50 = 2 + 3n

3n = 50 - 2

Further simplifying for n

3n = 48

n = 48/3

n = 16

Now, here we can find the sum of the n terms of the given A.P., using the formula,

S_n = (n/2)(a + 1)

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 n terms of an A.P., we get,

S_16 = (16/2)[5 + 50]

= 8(55)

= 440

Therefore, for the given A.P n = 16 and S_16 = 440

Concept: Sum of First n Terms of an AP
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 56.1 | Page 53