Math, asked by marciadacalano8, 6 hours ago

Solve for the following: 1. Find the 10th term in the sequence 2, 3, 4,… 2. Find the 20th term of the arithmetic progression 17,13,9,… 3. Find t20 if t1 = 6 and d = 15. 4. If a1 = 5, a7 = 17, and n = 7, find the common difference. 5. The 15th term of an arithmetic progression is 45. If the common difference is 3, find the first term.

Answers

Answered by mayanknagdali122993

Answer:

If a series is arithmetic the sum of the first n terms, denoted Sn , there are ways to find its sum without actually adding all of the terms.

To find the sum of the first n terms of an arithmetic series use the formula, n terms of an arithmetic sequence use the formula,

Sn=n(a1 + an)2 ,

where n is the number of terms, a1 is the first term and an is the last term.

The series 3+6+9+12+⋯+30 can be expressed as sigma notation ∑n=1103n . This expression is read as the sum of 3n as n goes from 1 to 10

Example 1:

Find the sum of the first 20 terms of the arithmetic series if a1=5 and a20=62 .

S20=20(5 + 62)2S20=670

Example 2:

Find the sum of the first 40 terms of the arithmetic sequence

2,5,8,11,14,⋯

First find the 40 th term:

a40=a1+(n−1)d =2+39(3)=119

Then find the sum:

Sn=n(a1+an)2S40=40(2 + 119)2=2420

Example 3:

Find the sum:

∑k=150(3k+2)

First find a1 and a50 :

a1=3(1)+2=5a20=3(50)+2=152

Then find the sum:

Sk=k(a1 + ak)2S50=50(5 + 152)2=3925

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