5.the 25th term of an ap is 100, and the common difference is 3. find the first term and the 5th term.\n6.in…

5.the 25th term of an ap is 100, and the common difference is 3. find the first term and the 5th term.\n6.in an ap, the first term is -6 and the 18th term is 48. find the common difference and the first five terms.\n7.if the 30th term of an ap is 120 and the first term is 0, find the common difference and write the first five terms.\n8.the 7th term of an ap is 25, and the 12th term is 50. find the common difference and the first term.

5.the 25th term of an ap is 100, and the common difference is 3. find the first term and the 5th term.\n6.in an ap, the first term is -6 and the 18th term is 48. find the common difference and the first five terms.\n7.if the 30th term of an ap is 120 and the first term is 0, find the common difference and write the first five terms.\n8.the 7th term of an ap is 25, and the 12th term is 50. find the common difference and the first term.

Answer

Explanation:

Step1: Use the formula for the nth term of an AP

The formula for the (n)th term of an arithmetic progression (AP) is (a_n=a_1+(n - 1)d), where (a_n) is the (n)th term, (a_1) is the first term, (n) is the term number, and (d) is the common difference.

Given (a_{25}=100), (n = 25), and (d = 3). Substitute these values into the formula: (a_{25}=a_1+(25 - 1)\times3) (100=a_1+24\times3) (100=a_1 + 72)

Step2: Solve for the first term (a_1)

Subtract 72 from both sides of the equation: (a_1=100 - 72) (a_1 = 28)

Step3: Find the 5th term (a_5)

Use the formula (a_n=a_1+(n - 1)d) with (n = 5), (a_1=28), and (d = 3) (a_5=28+(5 - 1)\times3) (a_5=28+4\times3) (a_5=28 + 12) (a_5=40)

Answer:

The first term (a_1 = 28) and the 5th term (a_5=40)