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:

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

Answer 2

   First 60 terms of the arithmetic sequence will be 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, 263, 268, 273, 278, 283, 288, 293, 298.

Arithmetic sequence:

•   If two consecutive terms of a sequence has a common

           difference 'd', sequence will be an arithmetic sequence and the

           explicit formula for the nth term of the sequence will be,

           $A_n=a+(n-1)d$

           Here, $a=$ First term

                     $n=$ nth term

                     $d=$ common difference

Given in the question,

Two terms $a_5=23, a_{20}=98$

If 5th term of the sequence is 23,

$23=a+(5-1)d$

$23=a+4d$  -------(1)

If 20th term of the sequence is 98,

$98=a+(20-1)d$

$98=a+19d$ ----------(2)

Subtract equation (1) from equation (2),

98 - 23 = a + 19d - (a + 4d)

75 = 15d

d = 5

Substitute the value of 'd' in equation (1),

23 = a + 4(5)

a = 23 - 20

a = 3

     Therefore, first 60 terms of the arithmetic sequence will be 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, 263, 268, 273, 278, 283, 288, 293, 298.

Learn more about an arithmetic sequence here,

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