Question

Find the sum of 25 terms of the arithmetic sequences 5,8,11---
​

Answer 1

Concept Introduction:

The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

Given:

Arithmetic sequences $5,8,11$---

​To Find:

We have to find the value of, sum of $25$ terms of the arithmetic sequence.

Solution:

According to the problem,

n=$25$; $a=5; d=3$

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

$25/2[2*5+(25-1)3]=25/2[10+72]=25/2*82=1025$

Final Answer:

The value of sum of $25$ terms are $1025$.

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Answer 2

Concept:

Sequence and Series: Arithmetic Progression

Given:

Given arithmetic sequence is 5, 8, 11, ------------

Find:

Sum of first 25 terms.

Solution:

Sum of first n terms of an AP is given by,

Sₙ = n/2[2a + (n- 1) d]

where n = number of terms

a = first term of the AP

d = common difference

We have AP 5, 8, 11, ---------

First term, a = 5

Common difference, d = a₂ - a₁

                                      = 8 - 5 = 3

Number of terms, n = 25

∴ S₂₅ = 25/2 [2(5) + (25 - 1)(3)]

         = 25/2 [ 10 + (24)(3)]

         = 25/2 [ 10 + 72]

         = 25/2 (82)

         = (25×82)/2

         = 1025

Hence, the sum of 25 terms of the arithmetic sequences 5,8,11--- is 1025.

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