# Find the sum: a-ba+b+3a-2ba+b+5a-3ba+b+ .... to 11 terms. - Mathematics

Sum

Find the sum: (a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) + .... to 11 terms.

#### Solution

Here, first term (A) = (a - b)/(a + b)

And common difference,

D = (3a - 2b)/(a + b) - (a - b)/(a + b) = (2a - b)/(a + b)

∵ Sum of n terms of an AP,

S_n = n/2[2A + (n - 1)D]

⇒ S_n = n/2{2((a - b))/((a + b)) + (n - 1) ((2a - b))/((a + b))}

= n/2{(2a - 2b + 2an - 2a - bn + b)/(a + b)}

= n/2((2an - bn - b)/(a + b))

∴ S_11 = 11/2{(2a(11) - b(11) - b)/(a + b)}

= 11/2((22a - 12b)/(a + b))

= (11(11a - 6b))/(a + b)

Concept: Sum of First n Terms of an A.P.
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 5 Arithematic Progressions
Exercise 5.3 | Q 21.(iii) | Page 53
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