Question

the sum of the AP 1+3+5+7+...........+25 is equal to..​

Answer 1

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Given ,

• The series is 1 + 3 + 5 + 7 + ......... + 25
• First term is 1
• Common difference (d) is (3 - 1) i.e 2
• Last term (l) is 25

We know that , the nth term of an AP is given by

$\large \mathtt{\fbox{ a_{n} = a + (n - 1)d }}$

Substitute the given values , we obtain

25 = 1 + (n - 1)2

24 = (n - 1)2

12 = n - 1

n = 13

Now , the sum of first n terms of an AP is given by

$\large \mathtt{\fbox{ sum= \frac{n}{2}(a + l) }}$

Substitute the given values , we obtain

Sum = 13/2 × (1 + 25)

Sum = 13/2 × 26

Sum = 13 × 13

Sum = 169

Hence , the sum of the given series is 169

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