the 3rd and 8th terms of an arithmetic progression (A.P) are -9 and 26 respectively.find the:a=common difference,b=first term,c=sum of 5th and 7th terms,d=product of 5th and 7th terms.
Using the definitions ....
a+2d = -9
a+7d = 26
subtract them:
5d = 35
d = 7 and a = -23
Now you can find any term in the sequence and should be able to answer
c) and d)
To find the common difference (a) in an arithmetic progression (A.P), you need to subtract the first term from the second term or any two consecutive terms.
In this case, the 3rd term is -9 and the 8th term is 26. So, we can find the common difference (a) by subtracting the 3rd term from the 8th term:
a = 26 - (-9)
a = 26 + 9
a = 35
Therefore, the common difference (a) is 35.
To find the first term (b) in the A.P, you can substitute the value of a (common difference) and any term of the sequence (e.g., the 3rd term) into the formula:
b = nth term - (n-1) * a
Using the formula, we can find the first term (b):
b = -9 - (3-1) * 35
b = -9 - 2 * 35
b = -9 - 70
b = -79
Therefore, the first term (b) is -79.
To find the sum of the 5th (n=5) and 7th (n=7) terms (c), you can use the formula for the nth term of an A.P:
nth term = a + (n-1) * d
Substituting n=5 and n=7 into the formula, we can find the 5th and 7th terms and calculate their sum (c):
5th term = -79 + (5-1) * 35
5th term = -79 + 4 * 35
5th term = -79 + 140
5th term = 61
7th term = -79 + (7-1) * 35
7th term = -79 + 6 * 35
7th term = -79 + 210
7th term = 131
c = 5th term + 7th term
c = 61 + 131
c = 192
Therefore, the sum of the 5th and 7th terms (c) is 192.
To find the product of the 5th and 7th terms (d), simply multiply the values we found for the 5th and 7th terms:
d = 61 * 131
d = 7991
Therefore, the product of the 5th and 7th terms (d) is 7991.