Question

Find the sum of 5+8+11+......to 10terms using formula
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Answer 1

Answer:

Given AP: 5+ 8+ 11+........10 terms

here, a = 5 , n= 10 , d =3

10th term = a + (n - 1) d

= 5 + (10 -1) 3

= 5+ 9 (3)

=5+27

therefore, 10th term=32

sum of 10 terms = n/2 ( a+ 10th term )

=10/2 ( 5+32)

= 5 ( 37 )

=185

therefore, sum of the given terms is 185

Answer 2

Given:

A sequence 5+8+11+....to 10terms which is in the form of A.P.

To find:

The sum of the 5+8+11+....to 10terms.

Solution:

The sum of 5+8+11+...to 10terms is 185.

To answer this question, we will follow the following steps:

As given,

We have a sequence

5+8+11+...to 10terms.

This forms an arithmetic progression (A.P.) in which the sum of terms 'S' is given by:

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

where 'd' is a common difference, 'a' is the first term, n = number of terms till nth term.

So,

in the sequence 5+8+11+...to 10terms.

a = 5, d = second term - first term = 8 - 5 = 3, n = 10

Now,

The sum of the first 10 terms is

$= \frac{10}{2} [2(5) + (10 - 1)3]$

$= 5(10 + 27)$

$= 5(37)$

$= 185$

Hence, the sum of the first 10 terms of the given sequence is 185.