Question

if the first term of an AP is 1 and the common difference is 2 then the sum of first 26 term is​

Answer 1

Solution

Given That:-

• First terms of A.P. (a) = 1
• Common difference (d) = 2

Find :-

• sum of first 26 term of A.P. series

Explanation

Using Formula,

★Sn = a/2 * [ 2a + (n-1)d]

So, Keep all above values

==> S26 = 1/2 * [ 2 * 1 + (26-1)2]

==> S26 = 1/2 * [ 2 + 25 * 2]

==> S26 = 1/2 * [ 2 + 50]

==> S26 = 1/2 * 100

==> S26 = 50

Hence

• Sum of 26 terms of A.P. will be = 50

_________________

Answer 2

$\sf\large{\underline{\underline{\blue{Question:-}}}}$

if the first term of an AP is 1 and the common difference is 2 then the sum of first 26 term is.

$\sf\large{\underline{\underline{\red{Given:-}}}}$

• 1st term.of A.P is = 1
• Common difference = 2

Or

• 1st term (a) =1
• common difference (d)=2

$\sf\large{\underline{\underline{\blue{To\:find:-}}}}$

• 26th term of an A.P=?

Or

• 26th term =$\bf S_n=?$

$\sf\large{\underline{\underline{\blue{Solution:-}}}}$

$\sf→ S_{26}=\frac{1}{2}[2×1+(26-1)2]\\\sf→ S_{26}=\frac{1}{2}[2+25×2]\\\sf→ S_{26}=\frac{1}{2}×100\\\sf→{\fbox{\underline{\purple{S_{26}=50}}}}</p><p>$

$\sf\large{\underline{\underline{\green{Hence:-}}}}$

• The 26th term of the A.P is = 50

$\sf\large{\underline{\underline{\red{Formula\: used:-}}}}$

$\sf→{\fbox{\underline{\underline{\red{S_n=\frac{1}{2}[2a+(n-1)d]}}}}}$