Question

If the 6th term of an A.P. is 46, find the sum of first 11 terms.​

Answer 1

Answer:

the sum is 506

Explanation:

given a6= 46

=>a+5d= 46——>(1)

therefore.

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

S11= 11/2[2a+(11-1)d]

S11=11/2[2a+10d]

S11= 11/2[2(a+5d)]

S11=11(46)

S11 = 506

Answer 2

The sum of the first 11 terms is​ 506.

Explanation:

• The sixth term of an Arithmetic Progression has been given as 46.

So, $a+5d=46$

• In order to find the sum of the first 11 terms, a formula has to be applied, which is:

$S_n=\frac{n}{2}[a+(n-1)d]$

∴ $S_{11}=\frac{11}{2}[2\times a(11-1)d]$

∴ $S_{11}=\frac{11}{2}(2a+10d)$

∴ $S_{11}=\frac{11}{2}(2a+5d)$

∴ $S_{11}=11\times46$

Hence, $S_{11}=506$