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ACT Exam  >  ACT Questions  >  If a, b, c, d are in H.P., then the value ofi... Start Learning for Free
If a, b, c, d are in H.P., then the value of is
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If a, b, c, d are in H.P., then the value ofisa)1b)2c)3d)4Correct answ...
Concept:
Arithmetic Progression: Sequence where the differences between every two consecutive terms are the same.
For example:- a, a +  d, a + 2d, ... are in AP.
Four terms that are in AP can be taken as
a - 3d, a - d, a + d, a + 3d
Harmonic mean (HM):  If a, b & c are in HP then,
1/a, 1/b, 1/c are in harmonic progression (AP). 
Calculation:
Given that, a, b, c, d are in H.P. then
 
Let these terms be (x - 3y), (x - y), (x + y), (x + 3y)
Hence,
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Adapted from The Varieties of Religious Experience by William James (1902)In the matter of religions, it is particularly easy distinguishing the too orders of question. Every religious phenomenon has its history and its derivation from natural antecedents. What is nowadays called the higher criticism of the Bible are only a study of the Bible from this existential point of view, neglected to much by the earlier church. Under just what biographic conditions did the sacred writers bring forth their various contributions to the holy volume? What had they exactly in their several individual minds, when they delivered their utterances? These are manifestly questions of historical fact, and one does not see how the answer to it can decide offhand the still further question: of what use should such a volume, with its manner of coming into existence so defined, be to us as a guide to life and a revelation? To answer this other question we must have already in our mind some sort of a general theory as to what the peculiarities in a thing should be which give it value for purposes of revelation; and this theory itself would be what I just called a spiritual judgment. Combining it with our existential judgment, we might indeed deduce another spiritual judgment as to the Bibles’ worth. Thus, if our theory of revelation-value were to affirm that any book, to possess it, must have been composed automatically or not by the free caprice of the writer, or that it must exhibit no scientific and historic errors and express no local or personal passions, the Bible would probably fare ill at our hands. But if, on the other hand, our theory should allow that a book may well be a revelation in spite of errors and passions and deliberate human composition, if only it be a true record of the inner experiences of great-souled persons wrestling with the crises of his fate, than the verdict would be much favorable. You see that the existential facts by itself are insufficient for determining the value; and the best adepts of the higher criticism accordingly never confound the existential with the spiritual problem. With the same conclusions of fact before them, some take one view, and some another, of the Bibles value as a revelation, according as their spiritual judgment as to the foundation of values differ.Q. Which is the best form of the underlined selection, "According as their spiritual judgment as to the foundation of values differ"?

Adapted from The Varieties of Religious Experience by William James (1902)In the matter of religions, it is particularly easy distinguishing the too orders of question. Every religious phenomenon has its history and its derivation from natural antecedents. What is nowadays called the higher criticism of the Bible are only a study of the Bible from this existential point of view, neglected to much by the earlier church. Under just what biographic conditions did the sacred writers bring forth their various contributions to the holy volume? What had they exactly in their several individual minds, when they delivered their utterances? These are manifestly questions of historical fact, and one does not see how the answer to it can decide offhand the still further question: of what use should such a volume, with its manner of coming into existence so defined, be to us as a guide to life and a revelation? To answer this other question we must have already in our mind some sort of a general theory as to what the peculiarities in a thing should be which give it value for purposes of revelation; and this theory itself would be what I just called a spiritual judgment. Combining it with our existential judgment, we might indeed deduce another spiritual judgment as to the Bibles’ worth. Thus, if our theory of revelation-value were to affirm that any book, to possess it, must have been composed automatically or not by the free caprice of the writer, or that it must exhibit no scientific and historic errors and express no local or personal passions, the Bible would probably fare ill at our hands. But if, on the other hand, our theory should allow that a book may well be a revelation in spite of errors and passions and deliberate human composition, if only it be a true record of the inner experiences of great-souled persons wrestling with the crises of his fate, than the verdict would be much favorable. You see that the existential facts by itself are insufficient for determining the value; and the best adepts of the higher criticism accordingly never confound the existential with the spiritual problem. With the same conclusions of fact before them, some take one view, and some another, of the Bibles value as a revelation, according as their spiritual judgment as to the foundation of values differ.Q. What is the best form of the underlined selection, "does not see how the answer to it can decide offhand"?

Adapted from The Varieties of Religious Experience by William James (1902)In the matter of religions, it is particularly easy distinguishing the too orders of question. Every religious phenomenon has its history and its derivation from natural antecedents. What is nowadays called the higher criticism of the Bible are only a study of the Bible from this existential point of view, neglected to much by the earlier church. Under just what biographic conditions did the sacred writers bring forth their various contributions to the holy volume? What had they exactly in their several individual minds, when they delivered their utterances? These are manifestly questions of historical fact, and one does not see how the answer to it can decide offhand the still further question: of what use should such a volume, with its manner of coming into existence so defined, be to us as a guide to life and a revelation? To answer this other question we must have already in our mind some sort of a general theory as to what the peculiarities in a thing should be which give it value for purposes of revelation; and this theory itself would be what I just called a spiritual judgment. Combining it with our existential judgment, we might indeed deduce another spiritual judgment as to the Bibles’ worth. Thus, if our theory of revelation-value were to affirm that any book, to possess it, must have been composed automatically or not by the free caprice of the writer, or that it must exhibit no scientific and historic errors and express no local or personal passions, the Bible would probably fare ill at our hands. But if, on the other hand, our theory should allow that a book may well be a revelation in spite of errors and passions and deliberate human composition, if only it be a true record of the inner experiences of great-souled persons wrestling with the crises of his fate, than the verdict would be much favorable. You see that the existential facts by itself are insufficient for determining the value; and the best adepts of the higher criticism accordingly never confound the existential with the spiritual problem. With the same conclusions of fact before them, some take one view, and some another, of the Bibles value as a revelation, according as their spiritual judgment as to the foundation of values differ.Q. What is the best version of the underlined selection, "the too orders of question"?

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If a, b, c, d are in H.P., then the value ofisa)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer?
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