Wierzycaz

2021-01-15

Find the 37th term of an arithmetic sequence whose second and third terms are −4 and 12.
If the fourth term of an arithmetic sequence is 17 and the second term is 3, find the 24th term.

ottcomn

Skilled2021-01-16Added 97 answers

Step 1
Given:
Second term $({a}_{2})=\text{}-4$
Third term $({a}_{3})=12$
Step 2
Used concept
${T}_{n}={a}_{1}\text{}+\text{}(n\text{}-\text{}1)d$
Where ${T}_{n}\text{}\to \text{}{n}^{(th)}\text{}\text{term}$

${a}_{1}\text{}\to \text{}{1}^{(st)}\text{}\text{term}$

$d\text{}\to \text{}\text{difference}\text{}=({a}_{2}\text{}-\text{}{a}_{1})=({a}_{3}\text{}-\text{}{a}_{2})$
Step 3
Apply the above concept it gives
$d={a}_{3}\text{}-\text{}{a}_{2}$

$d=12\text{}-\text{}(-4)$

$d=12\text{}+\text{}4=16$
now,
${a}_{1}={a}_{2}\text{}-\text{}d$

${a}_{1}=\text{}-4\text{}-\text{}16=\text{}-20$
Step 4
The ${37}^{(th)}$ term of the given arithmetic sequence will be
${T}_{37}=\text{}-20\text{}+\text{}(37\text{}-\text{}1)\text{}\times \text{}16$

$=\text{}-20\text{}+\text{}36\text{}\times \text{}16$

$=\text{}-20\text{}+\text{}576$

$=556$ (answer)

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