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An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of last 15 terms .?
Verified Answer
An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of ...
Solution :-
a = 5
d = 12 - 5 = 7
n = 50
an = a + (n - 1)d
an = 5 + (50 - 1)7
an = 5 + 49*7
an = 5 + 343
an = 348
Sum of the last 25 terms -
a = 348, d = - 7, n = 15
Sn = n/2[2a + (n - 1)d]
Sn = 15/2[2*348 + (15- 1) - 7]
Sn = 7.5[696 + (14 X - 7)]
Sn = 7.5[696 - 98]
Sn = 7.5*598
Sn = 4485
Sum of the last 15 term is 4485
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Most Upvoted Answer
An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of ...
A1=5,
d=12-5=7,
n=50,
a50=a+(n-1)d,
=5+(49)7=5+343=348,
a15=5+14(7)=5+98=103,
s15=15/2(5+103)
=15/2(108),
=15×54=810
d=12-5=7,
n=50,
a50=a+(n-1)d,
=5+(49)7=5+343=348,
a15=5+14(7)=5+98=103,
s15=15/2(5+103)
=15/2(108),
=15×54=810
Community Answer
An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of ...
Given:
An arithmetic progression (AP) with the first term (a) as 5, the common difference (d) as 12 - 5 = 7, and the number of terms (n) as 50.
To find:
The last term of the AP and the sum of the last 15 terms.
Solution:
Finding the last term:
The formula to find the nth term (Tn) of an AP is given by:
Tn = a + (n - 1)d
Substituting the given values, we have:
T50 = 5 + (50 - 1)7
T50 = 5 + 49 * 7
T50 = 5 + 343
T50 = 348
Therefore, the last term of the AP is 348.
Finding the sum of the last 15 terms:
The formula to find the sum of the first n terms (Sn) of an AP is given by:
Sn = (n/2)(2a + (n - 1)d)
We need to find the sum of the last 15 terms, so we will use the formula with n = 15.
Substituting the given values, we have:
S15 = (15/2)(2 * 5 + (15 - 1)7)
S15 = (15/2)(10 + 14 * 7)
S15 = (15/2)(10 + 98)
S15 = (15/2)(108)
S15 = 15 * 54
S15 = 810
Therefore, the sum of the last 15 terms of the AP is 810.
Summary:
The last term of the given arithmetic progression is 348. The sum of the last 15 terms of the AP is 810.
An arithmetic progression (AP) with the first term (a) as 5, the common difference (d) as 12 - 5 = 7, and the number of terms (n) as 50.
To find:
The last term of the AP and the sum of the last 15 terms.
Solution:
Finding the last term:
The formula to find the nth term (Tn) of an AP is given by:
Tn = a + (n - 1)d
Substituting the given values, we have:
T50 = 5 + (50 - 1)7
T50 = 5 + 49 * 7
T50 = 5 + 343
T50 = 348
Therefore, the last term of the AP is 348.
Finding the sum of the last 15 terms:
The formula to find the sum of the first n terms (Sn) of an AP is given by:
Sn = (n/2)(2a + (n - 1)d)
We need to find the sum of the last 15 terms, so we will use the formula with n = 15.
Substituting the given values, we have:
S15 = (15/2)(2 * 5 + (15 - 1)7)
S15 = (15/2)(10 + 14 * 7)
S15 = (15/2)(10 + 98)
S15 = (15/2)(108)
S15 = 15 * 54
S15 = 810
Therefore, the sum of the last 15 terms of the AP is 810.
Summary:
The last term of the given arithmetic progression is 348. The sum of the last 15 terms of the AP is 810.
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An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of last 15 terms .?
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An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of last 15 terms .? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of last 15 terms .? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of last 15 terms .?.
An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of last 15 terms .? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of last 15 terms .? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An AP 5,12,19.has 50 terms. Find its last term. Hence find the sum of last 15 terms .?.
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