# Find the Sum of the Following Arithmetic Progressions: 50, 46, 42, ... to 10 Terms - Mathematics

Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms

#### Solution

In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,

S_n =n/2 [2a + (n -1)d]

Where a = first term for the given A.P.

d = common difference of the given A.P

n =  number of terms

50, 46, 42, ... to 10 terms

Common difference of the A.P. (d)

= a_2 - a_1

= 46 - 50

= -4

Number of terms (n) = 10

First term for the given A.P. (a) = 50

So using the formula we get

S_10 = 10/2 [2(50) + (10 - 1)(-4)]

= (5)[100 + (9)(-4)]

= (5)[100 - 36]

= (5)[64]

= 320

Therefore the sum of first 10 terms for the given A.P is 320

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 1.1 | Page 30