Question

Two terms of an arithmetic sequence are a5=23 and a20=98. find the first 60 terms of the sequence

Answer 1

Answer:

$-37,-32,-27,-22,-17,-12,-7,-2,3,8,\\13,18,23,28,33,38,43,48,53,58\\63,68,73,78,83,88,93,98,103,108\\113,118,123,128,133,138,143,148,153,158\\163,168,173,178,183,188,193,198,203,208,\\213,218,223,228,233,238,243,248,253,258$

Step-by-step explanation:

The nth term of an arithmetic sequence is obtained using the formula:

$a_n=a+(n-1)d$

Given that: $a_5=23 and a_{20}=98.$

a_n=a+(n-1)d

$a_5=23=a+(5-1)d \implies a+4d=23\\a_{20}=98=a+(20-1)d \implies a+19d=98\\ We solve simultaneously :\\a+19d=98\\a+4d=23\\15d=75\\d=5\\Recall:a+4d=23\\a+4(15)=23\\a=23-60\\a=-37$

Therefore, the first 60 terms of the sequence are:

$-37,-32,-27,-22,-17,-12,-7,-2,3,8,\\13,18,23,28,33,38,43,48,53,58\\63,68,73,78,83,88,93,98,103,108\\113,118,123,128,133,138,143,148,153,158\\163,168,173,178,183,188,193,198,203,208,\\213,218,223,228,233,238,243,248,253,258$