Answer :

**Given:** S_{5} + S_{7} = 167

S_{10} = 235

**To find:** S_{20}

**Formula Used:**

Sum of “n” terms of an AP:

Where S_{n} is the sum of first n terms

n = no of terms

a = first term

d = common difference

**Explanation:**

Let the first term, common difference and the number of terms of an AP are a, d and n, respectively.

As,

S_{5} + S_{7} = 167

we have,

5(2a + 4d) + 7( 2a + 6d ) = 334

10a + 20d + 14a + 42d = 334

24a + 62d = 334

12a + 31d = 167

12a = 167 - 31d [ eqn 1]

Also,

S_{10} = 235

5[ 2a + 9d] = 235

2a + 9d = 47

12a + 54d = 282 [ multiplication by 6 both side]

167 - 31d + 54d = 282 [ using equation 1]

23d = 282 - 167

23d = 115

d = 5

using this value in equation 1

12a = 167 - 31(5 )

12a = 167 - 155

12a = 12

a = 1

Now

= 10[ 2 + 95]

= 970

So, the sum of first 20 terms is 970.

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