Find the sum of the terms from

Malachi Mullins

Malachi Mullins

Answered question

2022-04-07

Find the sum of the terms from a16 to a23 for the following sequence
7,10,13,16,

Answer & Explanation

Assorrymarf0cgr

Assorrymarf0cgr

Beginner2022-04-08Added 10 answers

The general term an of an arithmetic sequence is defined using the formula: an=a+(n1)d
The first term a=7
The common difference d=107=3
Substitute a=7, d=3 in the formula
an=a+(n1)d
=7+(n1)3
=7+3n3
=3n+4
Hence, an=3n+4
Calculate a16 by substituting n=16 in the general term.
an=3n+4
a16=3(16)+4
=48+4
=52
Calculate a23 by substituting n=23 in the general term.
an=3n+4
a23=3(23)+4
=69+4
=73
The total number of terms between a16 and a23 are 8. Let it be an arithmetic sequence, whose first term is a16 and the last term is a23.
The sum of these terms Sn:
Sn=n2[First term+L term]
S8=82[a16+a23]
=82[52+73]
=4×125
=500

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